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Journal articles on the topic 'Adjointness'

Author: Grafiati

Published: 4 June 2025

Last updated: 15 July 2025

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1

Hidaka, Takeru, and Fumio Hiroshima. "Self-adjointness of the semi-relativistic Pauli–Fierz Hamiltonian." Reviews in Mathematical Physics 27, no. 07 (2015): 1550015. http://dx.doi.org/10.1142/s0129055x15500154.

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The spinless semi-relativistic Pauli–Fierz Hamiltonian [Formula: see text] in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, Hf the free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli–Fierz model with a fixed total momentum P ∈ ℝd: [Formula: see text] is also proven for arbitrary P.

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2

Mulry, Philip S. "Adjointness in recursion." Annals of Pure and Applied Logic 32 (1986): 281–89. http://dx.doi.org/10.1016/0168-0072(86)90056-4.

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3

Menni, M., and C. Smith. "Modes of Adjointness." Journal of Philosophical Logic 43, no. 2-3 (2013): 365–91. http://dx.doi.org/10.1007/s10992-012-9266-y.

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4

KOLB, MARTIN. "ON THE STRONG UNIQUENESS OF SOME FINITE DIMENSIONAL DIRICHLET OPERATORS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 02 (2008): 279–93. http://dx.doi.org/10.1142/s0219025708003117.

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We prove essential self-adjointness of a class of Dirichlet operators in ℝn using the hyperbolic equation approach. This method allows one to prove essential self-adjointness under minimal conditions on the logarithmic derivative of the density and a condition of Muckenhoupt type on the density itself.

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5

Wu, Xiaohong, Junjie Huang, and Eerdun Buhe. "On Symplectic Self-Adjointness of Hamiltonian Operator Matrices." Symmetry 15, no. 12 (2023): 2163. http://dx.doi.org/10.3390/sym15122163.

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The symmetry of the spectrum and the completeness of the eigenfunction system of the Hamiltonian operator matrix have important applications in the symplectic Fourier expansion method in elasticity. However, the symplectic self-adjointness of Hamiltonian operator matrices is important to the characterization of the symmetry of the point spectrum. Therefore, in this paper, the symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied by using the spectral method of unbounded block operator matrices, and some sufficient conditions of the symplectic self-adjointness of infinite dimensional Hamiltonian operators are obtained. In addition, the necessary and sufficient conditions are also investigated for some special infinite dimensional Hamiltonian operators.

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6

Sandovici, Adrian. "Self-adjointness and skew-adjointness criteria involving powers of linear relations." Journal of Mathematical Analysis and Applications 470, no. 1 (2019): 186–200. http://dx.doi.org/10.1016/j.jmaa.2018.09.063.

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7

Wang, Aiping, Jerry Ridenhour, and Anton Zettl. "Construction of regular and singular Green's functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 1 (2012): 171–98. http://dx.doi.org/10.1017/s0308210510001630.

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The Green function of singular limit-circle problems is constructed directly for the problem, not as a limit of sequences of regular Green's functions. This construction is used to obtain adjointness and self-adjointness conditions which are entirely analogous to the regular case. As an application, a new and explicit formula for the Green function of the classical Legendre problem is found.

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8

Morsi, Nehad N. "Propositional calculus under adjointness." Fuzzy Sets and Systems 132, no. 1 (2002): 91–106. http://dx.doi.org/10.1016/s0165-0114(02)00108-2.

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9

Betti, Renato. "Adjointness in descent theory." Journal of Pure and Applied Algebra 116, no. 1-3 (1997): 41–47. http://dx.doi.org/10.1016/s0022-4049(96)00161-2.

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10

Ricci, Paolo Emilio. "ADJOINTNESS FOR SHEFFER POLYNOMIALS." Jnanabha 50, no. 01 (2020): 57–64. http://dx.doi.org/10.58250/jnanabha.2020.50107.

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In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them have been studied. In this article new sets of Sheffer polynomials are introduced defining a sort of adjointness property. As an application, we show the adjoint set of Actuarial polynomials and derive their main characteristics.

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11

Izumi, Kouji, Hideo Tanaka, and Kiyoji Asai. "Adjointness of fuzzy systems." Fuzzy Sets and Systems 20, no. 2 (1986): 211–21. http://dx.doi.org/10.1016/0165-0114(86)90078-3.

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12

Wang, Haifeng, and Yufeng Zhang. "Self-adjointness and conservation laws of Burgers-type equations." Modern Physics Letters B 35, no. 09 (2021): 2150161. http://dx.doi.org/10.1142/s021798492150161x.

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This paper focuses on the self-adjointness of some Burgers-type equations based on the existing definitions. It follows that the corresponding Frobenius Burgers-type equations are constructed by taking values in a commutative subalgebra [Formula: see text]. In order to investigate the self-adjointness of these Frobenius-type equations, we introduce a few additional notations and definitions. Additionally, the conservation laws are obtained of several equations studied by using symmetries.

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13

Letzter, Edward S. "ON CONTINUOUS AND ADJOINT MORPHISMS BETWEEN NON-COMMUTATIVE PRIME SPECTRA." Proceedings of the Edinburgh Mathematical Society 49, no. 2 (2006): 367–81. http://dx.doi.org/10.1017/s0013091504000628.

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AbstractWe study topological properties of the correspondence of prime spectra associated with a non-commutative ring homomorphism $R\rightarrow S$. Our main result provides criteria for the adjointness of certain functors between the categories of Zariski closed subsets of $\spec R$ and $\spec S$; these functors arise naturally from restriction and extension of scalars. When $R$ and $S$ are left Noetherian, adjointness occurs only for centralizing and ‘nearly centralizing’ homomorphisms.

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14

Chajda, Ivan, and Helmut Länger. "Residuation in orthomodular lattices." Topological Algebra and its Applications 5, no. 1 (2017): 1–5. http://dx.doi.org/10.1515/taa-2017-0001.

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Abstract We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one.

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15

Minlos, Robert Adol'fovich. "On Pointlike Interaction between Three Particles: Two Fermions and Another Particle." ISRN Mathematical Physics 2012 (July 30, 2012): 1–18. http://dx.doi.org/10.5402/2012/230245.

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The problem of construction of self-adjoint Hamiltonian for quantum system consisting of three pointlike interacting particles (two fermions with mass 1 plus a particle of another nature with mass m>0) was studied in many works. In most of these works, a family of one-parametric symmetrical operators {Hε,ε∈ℝ1} is considered as such Hamiltonians. In addition, the question about the self-adjointness of Hε is equivalent to the one concerning the self-adjointness of some auxiliary operators {𝒯l,l=0,1,…} acting in the space L2(ℝ+1,r2dr). In this work, we establish a simple general criterion of self-adjointness for operators 𝒯l and apply it to the cases l=0 and l=1. It turns out that the operator 𝒯l=0 is self-adjoint for any m, while the operator 𝒯l=1 is self-adjoint for m>m0, where the value of m0 is given explicitly in the paper.

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16

SCHRÖDER, LUTZ, and PAULO MATEUS. "Universal aspects of probabilistic automata." Mathematical Structures in Computer Science 12, no. 4 (2002): 481–512. http://dx.doi.org/10.1017/s0960129502003614.

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Frequently, mathematical structures of a certain type and their morphisms fail to form a category for lack of composability of the morphisms; one example of this problem is the class of probabilistic automata when equipped with morphisms that allow restriction as well as relabelling. The proper mathematical framework for this situation is provided by a generalisation of category theory in the shape of the so-called precategories, which are introduced and studied in this paper. In particular, notions of adjointness, weak adjointness and partial adjointness for precategories are presented and justified in detail. This makes it possible to use universal properties as characterisations of well-known basic constructions in the theory of (generative) probabilistic automata: we show that accessible automata and decision trees, respectively, form coreflective subprecategories of the precategory of probabilistic automata. Moreover, the aggregation of two automata is identified as a partial product, whereas restriction and interconnection of automata are recognised as Cartesian lifts.

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17

Sadybekov, Makhmud A. "Stable difference scheme for a nonlocal boundary value heat conduction problem." e-Journal of Analysis and Applied Mathematics 1, no. 1 (2018): 1–10. http://dx.doi.org/10.2478/ejaam-2018-0001.

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AbstractIn this paper, a new finite difference method to solve nonlocal boundary value problems for the heat equation is proposed. The most important feature of these problems is the non-self-adjointness. Because of the non-self-adjointness, major difficulties occur when applying analytical and numerical solution techniques. Moreover, problems with boundary conditions that do not possess strong regularity are less studied. The scope of the present paper is to justify possibility of building a stable difference scheme with weights for mentioned type of problems above.

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18

BÍLKOVÁ, MARTA, JIŘÍ VELEBIL, and YDE VENEMA. "On monotone modalities and adjointness." Mathematical Structures in Computer Science 21, no. 2 (2011): 383–416. http://dx.doi.org/10.1017/s0960129510000514.

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We fix a logical connection (Stone ˧ Pred : Setop → BA given by 2 as a schizophrenic object) and study coalgebraic modal logic that is induced by a functor T: Set → Set that is finitary and standard and preserves weak pullbacks and finite sets. We prove that for any such T, the cover modality nabla is a left (and its dual delta is a right) adjoint relative to ω. We then consider monotone unary modalities arising from the logical connection and show that they all are left (or right) adjoints relative to ω.

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19

Thielecke, Hayo. "Continuation Semantics and Self-adjointness." Electronic Notes in Theoretical Computer Science 6 (1997): 348–64. http://dx.doi.org/10.1016/s1571-0661(05)80149-5.

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20

Amorim, Érik, and Eric A. Carlen. "Complete positivity and self-adjointness." Linear Algebra and its Applications 611 (February 2021): 389–439. http://dx.doi.org/10.1016/j.laa.2020.10.038.

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21

Willis, J. R. "Effective constitutive relations for waves in composites and metamaterials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2131 (2011): 1865–79. http://dx.doi.org/10.1098/rspa.2010.0620.

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Definitions of ‘effective fields’ for a randomly inhomogeneous material are offered, which guarantee automatic satisfaction of the equations of motion. The important case of a medium with periodic microstructure is included. In this special case, the definitions are completely explicit and can be applied without reference to random media. The presentation is mostly expressed in terms of electromagnetic waves. The reasoning is applicable also to other types of waves and its realization for elastodynamics is briefly outlined towards the end. Some of the effective fields are defined directly as ensemble averages, ensuring the exact satisfaction of the equations of motion, but the effective ‘kinematic’ fields to which they are related are defined more generally, as weighted averages. The main result of this work is an explicit formula for the tensor of effective properties. The important issue of uniqueness (or not) of the effective properties is explained and resolved. Self-adjointness of the original problem is not assumed. An attractive feature of the formulation is that self-adjointness at the local level implies self-adjointness at the level of the ‘effective medium’.

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22

Wang, Haifeng, and Yufeng Zhang. "Self-Adjointness and Conservation Laws of Frobenius Type Equations." Symmetry 12, no. 12 (2020): 1987. http://dx.doi.org/10.3390/sym12121987.

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The Frobenius KDV equation and the Frobenius KP equation are introduced, and the Frobenius Kompaneets equation, Frobenius Burgers equation and Frobenius Harry Dym equation are constructed by taking values in a commutative subalgebra Z2ε in the paper. The five equations are selected as examples to help us study the self-adjointness of Frobenius type equations, and we show that the first two equations are quasi self-adjoint and the last three equations are nonlinear self-adjointness. It follows that we give the symmetries of the Frobenius KDV and the Frobenius KP equation in order to construct the corresponding conservation laws.

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23

Benhellal, Badreddine, Konstantin Pankrashkin, and Mahdi Zreik. "On the self-adjointness of two-dimensional relativistic shell interactions." Journal of Operator Theory 93, no. 2 (2025): 569–91. https://doi.org/10.7900/jot.2023jul27.2447.

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We discuss the self-adjointness of the two-dimensional Dirac operator with a transmission condition along a closed Lipschitz curve. The new self-adjointness condition includes and extends all previous results for this class of problems. The study is particularly precise for the case of curvilinear polygons, as the angles can be taken into account in an explicit way. In particular, if the curve is a curvilinear polygon with obtuse angles, then there is a unique self-adjoint realization with domain contained in H1/2 for the full range of non-critical coefficients in the transmission condition.

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24

Vogel, Hans-Jürgen. "Adjointness between theories and strict theories." Discussiones Mathematicae - General Algebra and Applications 23, no. 2 (2003): 163. http://dx.doi.org/10.7151/dmgaa.1071.

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25

Ibragimov, N. H. "Nonlinear self-adjointness and conservation laws." Journal of Physics A: Mathematical and Theoretical 44, no. 43 (2011): 432002. http://dx.doi.org/10.1088/1751-8113/44/43/432002.

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26

Takaesu, Toshimitsu. "Essential Self-Adjointness of Anticommutative Operators." Journal of Mathematics 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/265349.

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The self-adjoint extensions of symmetric operators satisfying anticommutation relations are considered. It is proven that an anticommutative type of the Glimm-Jaffe-Nelson commutator theorem follows. Its application to an abstract Dirac operator is also considered.

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27

Coutinho, F. AB, Y. Nogami, L. Tomio, and F. M. Toyama. "Energy-dependent point interaction: Self-adjointness." Canadian Journal of Physics 84, no. 11 (2006): 991–1005. http://dx.doi.org/10.1139/p06-086.

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Recently, we constructed an energy-dependent point interaction (EDPI) in its most general form in one-dimensional quantum mechanics. In this paper, we show that stationary solutions of the Schrodinger equation with the EDPI form a complete set. Then any nonstationary solution of the time-dependent Schrodinger equation can be expressed as a linear combination of stationary solutions. This, however, does not necessarily mean that the EDPI is self-adjoint and the time-development of the nonstationary state is unitary. The EDPI is self-adjoint provided that the stationary solutions are all orthogonal to one another. We illustrate situations in which this orthogonality condition is not satisfied.PACS Nos.: 03.65.–w, 03.65.Nk, 03.65.Ge

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28

Magajna, Bojan, Marko Petkovšek, and Aleksej Turnšek. "An operator inequality and self-adjointness." Linear Algebra and its Applications 377 (January 2004): 181–94. http://dx.doi.org/10.1016/j.laa.2003.08.007.

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29

Jeon, In Ho, In Hyoun Kim, Kotaro Tanahashi, and Atsushi Uchiyama. "Conditions Implying Self-adjointness of Operators." Integral Equations and Operator Theory 61, no. 4 (2008): 549–57. http://dx.doi.org/10.1007/s00020-008-1598-1.

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30

Gandarias, M. L. "Nonlinear self-adjointness through differential substitutions." Communications in Nonlinear Science and Numerical Simulation 19, no. 10 (2014): 3523–28. http://dx.doi.org/10.1016/j.cnsns.2014.02.013.

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31

Much, Albert. "Self-adjointness of deformed unbounded operators." Journal of Mathematical Physics 56, no. 9 (2015): 093501. http://dx.doi.org/10.1063/1.4929662.

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32

Liskevich, V. A., and Yu A. Semenov. "Self-adjointness conditions for Dirichlet operators." Ukrainian Mathematical Journal 42, no. 2 (1990): 253–57. http://dx.doi.org/10.1007/bf01071027.

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33

Le Merdy, C. "Self adjointness criteria for operator algebras." Archiv der Mathematik 74, no. 3 (2000): 212–20. http://dx.doi.org/10.1007/s000130050433.

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34

Zhu, Chengjun, and John R. Klauder. "The self-adjointness of Hermitian Hamiltonians." Foundations of Physics 23, no. 4 (1993): 617–31. http://dx.doi.org/10.1007/bf01883769.

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35

Anné, Colette, Hela Ayadi, Yassin Chebbi, and Nabila Torki-Hamza. "Self-adjointness of magnetic Laplacians on triangulations." Filomat 37, no. 11 (2023): 3527–50. https://doi.org/10.2298/fil2311527a.

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The notions of magnetic difference operator or magnetic exterior derivative defined on weighted graphs are discrete analogues of the notion of covariant derivative on sections of a fibre bundle and its extension on differential forms. In this paper, we extend these notions to certain 2-simplicial complexes called triangulations, in a manner compatible with changes of gauge. Then we study the magnetic Gaus-Bonnet operator naturally defined in this context and introduce the geometric hypothesis of ??completeness which ensures the essential self-adjointness of this operator. This gives also the essential self-adjointness of the magnetic Laplacian on triangulations. Finally we introduce an hypothesis of bounded curvature for the magnetic potential which permits to caracterize the domain of the self-adjoint extension.

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36

LONG, HONGWEI, and ISABEL SIMÃO. "A NOTE ON THE ESSENTIAL SELF-ADJOINTNESS OF ORNSTEIN–UHLENBECK OPERATORS PERTURBED BY A DISSIPATIVE DRIFT AND A POTENTIAL." Infinite Dimensional Analysis, Quantum Probability and Related Topics 07, no. 02 (2004): 249–59. http://dx.doi.org/10.1142/s0219025704001621.

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We prove the essential self-adjointness of Ornstein–Uhlenbeck operators perturbed by a dissipative drift and a potential with polynomial growth, by establishing certain gradient estimates and using Berezanskii's parabolic criterion.

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37

Miao, Shu, Zi-Yi Yin, Zi-Rui Li, Chen-Yang Pan, and Guang-Mei Wei. "An Analysis of the Lie Symmetry and Conservation Law of a Variable-Coefficient Generalized Calogero–Bogoyavlenskii–Schiff Equation in Nonlinear Optics and Plasma Physics." Mathematics 12, no. 22 (2024): 3619. http://dx.doi.org/10.3390/math12223619.

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In this paper, the symmetries and conservation laws of a variable-coefficient generalized Calogero–Bogoyavlenskii–Schiff (vcGCBS) equation are investigated by modeling the propagation of long waves in nonlinear optics, fluid dynamics, and plasma physics. A Painlevé analysis is applied using the Kruskal-simplified form of the Weiss–Tabor–Carnevale (WTC) method, which shows that the vcGCBS equation does not possess the Painlevé property. Under the compatibility condition (a1(t)=a2(t)), infinitesimal generators and a symmetry analysis are presented via the symbolic computation program designed. With the Lagrangian, the adjoint equation is analyzed, and the vcGCBS equation is shown to possess nonlinear self-adjointness. Based on its nonlinear self-adjointness, conservation laws for the vcGCBS equation are derived by means of Ibragimov’s conservation theorem for each Lie symmetry.

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38

Clark, Steve, and Fritz Gesztesy. "On Povzner–Wienholtz-type self-adjointness results for matrix-valued Sturm–Liouville operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 4 (2003): 747–58. http://dx.doi.org/10.1017/s0308210500002651.

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39

Silenko, Alexander J. "Hermiticity and Self-Adjointness in Quantum Mechanics." Nonlinear Phenomena in Complex Systems 24, no. 1 (2021): 84–94. http://dx.doi.org/10.33581/1561-4085-2021-24-1-84-94.

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Hamiltonians in the geveralized Feshbach-Villars and Foldy-Wouthuysen representations describing an interaction of a scalar particle with electromagnetic fields in the Minkowski spacetime are self-adjoint and Hermitian (or pseudo-Hermitian) when they are presented in terms of operators of covariant derivatives. When one uses curvilinear coordinates in special relativity, the transition to the canonical momentum operator does not change these properties. When the curvilinear coordinates are applied in general relativity, the corresponding transition to the canonical momentum operator leads to the seeming non- Hermiticity of the Hamiltonians. Since the Hamiltonians remain in fact Hermitian, this seeming non-Hermiticity should not be eliminated by any nonunitary transformation.

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40

GIRI, PULAK RANJAN. "SELF-ADJOINTNESS OF GENERALIZED MIC–KEPLER SYSTEM." Modern Physics Letters A 22, no. 31 (2007): 2365–77. http://dx.doi.org/10.1142/s0217732307022530.

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We have studied the self-adjointness of generalized MIC–Kepler Hamiltonian, obtained from the formally self-adjoint generalized MIC–Kepler Hamiltonian. We have shown that for [Formula: see text], the system admits a one-parameter family of self-adjoint extensions and for [Formula: see text] but [Formula: see text], it also has a one-parameter family of self-adjoint extensions.

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41

Dhahri, Ameur. "Self-adjointness and boundedness in quadratic quantization." Journal of Mathematical Physics 55, no. 5 (2014): 052103. http://dx.doi.org/10.1063/1.4878497.

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42

Duclos, Pierre, and Arne Jensen. "On self-adjointness of singular Floquet Hamiltonians." Journal of Physics A: Mathematical and Theoretical 43, no. 47 (2010): 474019. http://dx.doi.org/10.1088/1751-8113/43/47/474019.

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43

Jorgensen, Palle E. T. "Essential self-adjointness of the graph-Laplacian." Journal of Mathematical Physics 49, no. 7 (2008): 073510. http://dx.doi.org/10.1063/1.2953684.

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44

Morsi, Nehad N., and Elewa M. Roshdy. "Issues on adjointness in multiple-valued logics." Information Sciences 176, no. 19 (2006): 2886–909. http://dx.doi.org/10.1016/j.ins.2005.08.005.

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45

Sitenko, Yu A., and V. M. Gorkavenko. "Self-adjointness, confinement and the Casimir effect." Facta universitatis - series: Physics, Chemistry and Technology 14, no. 3 (2016): 319–35. http://dx.doi.org/10.2298/fupct1603319s.

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An influence of a classical magnetic field on the vacuum of the quantized charged spinor matter field confined between two parallel material plates is studied. In the case of the uniform magnetic field transverse to the plates, the Casimir effect is shown to be repulsive, independently of a choice of boundary conditions and of a distance between the plates.

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46

Ahmed, Zafar. "Pseudo-reality and pseudo-adjointness of Hamiltonians." Journal of Physics A: Mathematical and General 36, no. 41 (2003): 10325–33. http://dx.doi.org/10.1088/0305-4470/36/41/005.

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47

Ellis, Eugenia. "Equivariant algebraic kk -theory and adjointness theorems." Journal of Algebra 398 (January 2014): 200–226. http://dx.doi.org/10.1016/j.jalgebra.2013.09.023.

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48

Lukovskii, I. A., and A. N. Timokha. "Self-adjointness of a certain integrodifferential operator." Ukrainian Mathematical Journal 42, no. 3 (1990): 375–76. http://dx.doi.org/10.1007/bf01057029.

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49

LEMLE, LUDOVIC DAN. "On the L^∞-uniqueness of multidimensional Nelson’s diffusion." Carpathian Journal of Mathematics 30, no. 2 (2014): 209–15. http://dx.doi.org/10.37193/cjm.2014.02.08.

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In this paper we study the uniqueness in the sense of the essential self-adjointness for the generator of Nelson’s diffusion on L∞. As consequence it is obtained the L1 -uniqueness of weak solutions for the associated FokkerPlanck-Kolmogorov equation.

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50

Xu, Guixin, and Meirong Zhang. "Relationships between Perturbations of a Linear Relation and Its Operator Part." Discrete Dynamics in Nature and Society 2022 (December 14, 2022): 1–12. http://dx.doi.org/10.1155/2022/9134363.

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In this study, we establish some relationships between perturbations of a linear relation and its operator part by constructing an operator, which is induced by two linear relations including their closedness, hermiticity, self-adjointness, various spectra, defect indices, and perturbation terms.

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