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Journal articles on the topic 'Nonselfadjoint operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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1

Kukushkin, Maksim V. "On One Method of Studying Spectral Properties of Non-selfadjoint Operators." Abstract and Applied Analysis 2020 (September 1, 2020): 1–13. http://dx.doi.org/10.1155/2020/1461647.

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In this paper, we explore a certain class of Non-selfadjoint operators acting on a complex separable Hilbert space. We consider a perturbation of a nonselfadjoint operator by an operator that is also nonselfadjoint. Our consideration is based on known spectral properties of the real component of a nonselfadjoint compact operator. Using a technique of the sesquilinear forms theory, we establish the compactness property of the resolvent and obtain the asymptotic equivalence between the real component of the resolvent and the resolvent of the real component for some class of nonselfadjoint operat

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2

Livšic, M. S. "On commuting nonselfadjoint operators." Integral Equations and Operator Theory 9, no. 1 (1986): 121–33. http://dx.doi.org/10.1007/bf01257065.

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3

Gil, M. I. "Positive Invertibility of Nonselfadjoint Operators." Positivity 8, no. 3 (2004): 243–56. http://dx.doi.org/10.1007/s11117-004-5372-6.

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4

Abbaoui, Lyazid, and Latifa Debbi. "An application of the nonselfadjoint operators theory in the study of stochastic processes." Journal of Applied Mathematics and Stochastic Analysis 2004, no. 2 (2004): 149–57. http://dx.doi.org/10.1155/s1048953304305034.

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The theory of operator colligations in Hilbert spaces gives rise to certain models for nonselfadjoint operators, called triangular models. These models generalize the spectral decomposition of selfadjoint operators. In this paper, we use the triangular model to obtain the correlation function (CF) of a nonstationary linearly representable stochastic process for which the corresponding operator is simple, dissipative, nonselfadjoint of rank 1, and has real spectrum. As a generalization, we represent the infinitesimal correlation function (ICF) of a nonhomogeneous linearly representable stochast

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5

Borisova, Galina S., and Kiril P. Kirchev. "Solitonic combinations and commuting nonselfadjoint operators." Journal of Mathematical Analysis and Applications 424, no. 1 (2015): 21–48. http://dx.doi.org/10.1016/j.jmaa.2014.10.083.

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6

Gil’, Michael. "Spectral approximations of unbounded nonselfadjoint operators." Analysis and Mathematical Physics 3, no. 1 (2012): 37–44. http://dx.doi.org/10.1007/s13324-012-0037-2.

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7

Guebbai, Hamza, Sami Segni, Mourad Ghiat, and Meryem Zaddouri. "Pseudo-spectral study for a class of convection-diffusion operators." Reviews in Mathematical Physics 31, no. 01 (2019): 1950001. http://dx.doi.org/10.1142/s0129055x19500016.

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Using adequate strategies, we localize the spectrum of a class of differential operators. We consider the conditioning of the pseudo-spectrum for a family of nonselfadjoint convection-diffusion operators defined on an unbounded open set of [Formula: see text].

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8

Johnson, Mathew A., and Kevin Zumbrun. "Convergence of Hill's Method for Nonselfadjoint Operators." SIAM Journal on Numerical Analysis 50, no. 1 (2012): 64–78. http://dx.doi.org/10.1137/100809349.

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9

Kozhukhar’, P. A. "Point spectrum of singular nonselfadjoint differential operators." Functional Analysis and Its Applications 25, no. 3 (1991): 227–28. http://dx.doi.org/10.1007/bf01085495.

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10

Yurko, Vjacheslav Anatoljevich. "Spectral analysis for differential operators with singularities." Abstract and Applied Analysis 2004, no. 2 (2004): 165–82. http://dx.doi.org/10.1155/s1085337504310055.

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Nonselfadjoint boundary value problems for second-order differential equations on a finite interval with nonintegrable singularities inside the interval are considered under additional sewing conditions for solutions at the singular point. We study properties of the spectrum, prove the completeness of eigen- and associated functions, and investigate the inverse problem of recovering the boundary value problem from its spectral characteristics.

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11

Duman, Melda, Alp Kiraç, and Oktay Veliev. "Asymptotic formulas with arbitrary order for nonselfadjoint differential operators." Studia Scientiarum Mathematicarum Hungarica 44, no. 3 (2007): 391–409. http://dx.doi.org/10.1556/sscmath.2007.1026.

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We obtain asymptotic formulas with arbitrary order of accuracy for the eigenvalues and eigenfunctions of a nonselfadjoint ordinary differential operator of order n whose coefficients are Lebesgue integrable on [0, 1] and the boundary conditions are strongly regular. The orders of asymptotic formulas are independent of smoothness of the coefficients.

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12

Freiling, G., and V. Yurko. "Boundary value problems with regular singularities and singular boundary conditions." International Journal of Mathematics and Mathematical Sciences 2005, no. 9 (2005): 1481–95. http://dx.doi.org/10.1155/ijmms.2005.1481.

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Singular boundary conditions are formulated for nonselfadjoint Sturm-Liouville operators with singularities and turning points. For boundary value problems with singular boundary conditions, properties of the spectrum are studied and the completeness of the system of root functions is proved.

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13

Borisova, Galina. "Sturm - Liouville systems and nonselfadjoint operators, presented as couplings of dissipative and antidissipative operators with real absolutely continuous spectra." Annual of Konstantin Preslavsky University of Shumen, Faculty of mathematics and informatics XXIII C (2022): 11–21. http://dx.doi.org/10.46687/wxfc2019.

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This paper is a continuation of the considerations of the paper [1] and it presents the connection between Sturm-Liouville systems and Livšic operator colligations theory. An usefull representation of solutions of Sturm - Liouville systems is obtained using the resolvent of operators from a large class of nonselfadjoint nondissipative operators, presented as couplings of dissipative and antidissipative operators with real spectra. A connection between Sturm-Liouville systems and the inner state of the corresponding open system of operators from the considered class is presented.

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14

Hitrik, M., J. (Johannes) Sjöstrand, and S. V. Ngoc. "Diophantine tori and spectral asymptotics for nonselfadjoint operators." American Journal of Mathematics 129, no. 1 (2007): 105–82. http://dx.doi.org/10.1353/ajm.2007.0001.

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15

Yilmaz, Bülent, and O. A. Veliev. "Asymptotic formulas for Dirichlet boundary value problems." Studia Scientiarum Mathematicarum Hungarica 42, no. 2 (2005): 153–71. http://dx.doi.org/10.1556/sscmath.42.2005.2.3.

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In this article we obtain asymptotic formulas of arbitrary order for eigenfunctions and eigenvalues of the nonselfadjoint Sturm-Liouville operators with Dirichlet boundary conditions, when the potential is a summable function. Then using these we compute the main part of the eigenvalues in special cases.

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16

Maryushenkov, Stanislav Vladimirovich. "The Conditions of Invertibility of a Class Nonselfadjoint Operators." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 12, no. 4 (2012): 14–19. http://dx.doi.org/10.18500/1816-9791-2012-12-4-14-19.

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17

Allahverdiev, Bilender P. "NONSELFADJOINT SINGULAR STURM-LIOUVILLE OPERATORS IN LIMIT-CIRCLE CASE." Taiwanese Journal of Mathematics 16, no. 6 (2012): 2035–52. http://dx.doi.org/10.11650/twjm/1500406837.

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18

Nonnenmacher, Stéphane, and Martin Vogel. "Local eigenvalue statistics of one-dimensional random nonselfadjoint pseudodifferential operators." Journal of the European Mathematical Society 23, no. 5 (2021): 1521–612. http://dx.doi.org/10.4171/jems/1039.

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19

Pinsky, Ross G. "A Generalized Dirichlet Principle for Second Order Nonselfadjoint Elliptic Operators." SIAM Journal on Mathematical Analysis 19, no. 1 (1988): 204–13. http://dx.doi.org/10.1137/0519015.

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20

Saltan, Suna, and Bilender P. Allahverdiev. "Spectral analysis of nonselfadjoint Schrödinger operators with a matrix potential." Journal of Mathematical Analysis and Applications 303, no. 1 (2005): 208–19. http://dx.doi.org/10.1016/j.jmaa.2004.08.031.

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21

Hitrik, Michael, and Johannes Sjöstrand. "Nonselfadjoint Perturbations of Selfadjoint Operators in Two Dimensions II. Vanishing Averages." Communications in Partial Differential Equations 30, no. 7 (2005): 1065–106. http://dx.doi.org/10.1081/pde-200064447.

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22

Shubov, Marianna A. "Nonselfadjoint operators generated by the equation of a nonhomogeneous damped string." Transactions of the American Mathematical Society 349, no. 11 (1997): 4481–99. http://dx.doi.org/10.1090/s0002-9947-97-02044-8.

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23

Stepin, S. A. "Complete Wave Operators in Nonselfadjoint Kato Model of Smooth Perturbation Theory." Russian Journal of Mathematical Physics 26, no. 1 (2019): 94–108. http://dx.doi.org/10.1134/s1061920819010102.

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24

Syroid, I. P. P. "On a method of defining the Fourier transform of nonselfadjoint operators." Journal of Soviet Mathematics 66, no. 6 (1993): 2562–64. http://dx.doi.org/10.1007/bf01097857.

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25

PONGE, RAPHAËL. "SPECTRAL ASYMMETRY, ZETA FUNCTIONS, AND THE NONCOMMUTATIVE RESIDUE." International Journal of Mathematics 17, no. 09 (2006): 1065–90. http://dx.doi.org/10.1142/s0129167x06003825.

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In this paper we study the spectral asymmetry of (possibly nonselfadjoint) elliptic ΨDO's in terms of the difference of zeta functions coming from different cuttings. Refining previous formulas of Wodzicki in the case of odd class elliptic ΨDO's, our main results have several consequence concerning the local independence with respect to the cutting, the regularity at integer points of eta functions and a geometric expression for the spectral asymmetry of Dirac operators which, in particular, yields a new spectral interpretation of the Einstein–Hilbert action in gravity.

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26

Solel, Baruch. "Algebras of Analytic Operators associated with a Periodic Flow on a Von Neumann Algebra." Canadian Journal of Mathematics 37, no. 3 (1985): 405–29. http://dx.doi.org/10.4153/cjm-1985-024-3.

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Let M be a σ-finite von Neumann algebra and {σt}t∊T be a σ-weakly continuous representation of the unit circle, T, as *-automorphisms of M. Let H∞(σ) be the set of all x ∊ M such thatThe structure of H∞(σ) was studied by several authors (see [2-13]).The main object of this paper is to study the σ-weakly closed subalgebras of M that contain H∞(σ). In [12] this was done for the special case where H∞(σ) is a nonselfadjoint crossed product.Let Mn, for n ∊ Z, be the set of all x ∊ M such that

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27

Pellicer, Marta. "Generalized Convergence and Uniform Bounds for Semigroups of Restrictions of Nonselfadjoint Operators." Journal of Dynamics and Differential Equations 22, no. 3 (2010): 399–411. http://dx.doi.org/10.1007/s10884-010-9184-z.

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28

Baranov, Anton D., and Dmitry V. Yakubovich. "Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators." Advances in Mathematics 302 (October 2016): 740–98. http://dx.doi.org/10.1016/j.aim.2016.07.020.

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29

Boĭmatov, K. Kh, and A. G. Kostyuchenko. "SPECTRAL ASYMPTOTICS OF NONSELFADJOINT ELLIPTIC SYSTEMS OF DIFFERENTIAL OPERATORS IN BOUNDED DOMAINS." Mathematics of the USSR-Sbornik 71, no. 2 (1992): 517–31. http://dx.doi.org/10.1070/sm1992v071n02abeh002135.

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30

Allakhverdiev, B. P. "ON THE THEORY OF NONSELFADJOINT OPERATORS OF SCHRÖDINGER TYPE WITH A MATRIX POTENTIAL." Russian Academy of Sciences. Izvestiya Mathematics 41, no. 2 (1993): 193–205. http://dx.doi.org/10.1070/im1993v041n02abeh002258.

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31

Yurko, V. A. "RECOVERY OF NONSELFADJOINT DIFFERENTIAL OPERATORS ON THE HALF-LINE FROM THE WEYL MATRIX." Mathematics of the USSR-Sbornik 72, no. 2 (1992): 413–38. http://dx.doi.org/10.1070/sm1992v072n02abeh002146.

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32

Bögli, Sabine, and Marco Marletta. "Essential numerical ranges for linear operator pencils." IMA Journal of Numerical Analysis 40, no. 4 (2019): 2256–308. http://dx.doi.org/10.1093/imanum/drz049.

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Abstract We introduce concepts of essential numerical range for the linear operator pencil $\lambda \mapsto A-\lambda B$. In contrast to the operator essential numerical range, the pencil essential numerical ranges are, in general, neither convex nor even connected. The new concepts allow us to describe the set of spectral pollution when approximating the operator pencil by projection and truncation methods. Moreover, by transforming the operator eigenvalue problem $Tx=\lambda x$ into the pencil problem $BTx=\lambda Bx$ for suitable choices of $B$, we can obtain nonconvex spectral enclosures f

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33

Shubov, Marianna A., and Cheryl A. Peterson. "Asymptotic analysis of nonselfadjoint operators generated by coupled Euler-Bernoulli and Timoshenko beam model." Mathematische Nachrichten 267, no. 1 (2004): 88–109. http://dx.doi.org/10.1002/mana.200310155.

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34

Tersenov, Ar S. "Solvability of the lyapunov equation for nonselfadjoint second-order differential operators with nonlocal boundary conditions." Siberian Mathematical Journal 39, no. 5 (1998): 1026–42. http://dx.doi.org/10.1007/bf02672926.

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35

Tretter, Christiane. "Nonselfadjoint spectral problems for linear pencilsN-?P of ordinary differential operators with ?-linear boundary conditions: Completeness results." Integral Equations and Operator Theory 26, no. 2 (1996): 222–48. http://dx.doi.org/10.1007/bf01191859.

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36

Tersenov, Aris. "On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions." Annales Polonici Mathematici 77, no. 1 (2001): 79–104. http://dx.doi.org/10.4064/ap77-1-7.

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37

Shubov, Marianna A. "Asymptotic Representations for Root Vectors of Nonselfadjoint Operators and Pencils Generated by an Aircraft Wing Model in Subsonic Air Flow." Journal of Mathematical Analysis and Applications 260, no. 2 (2001): 341–66. http://dx.doi.org/10.1006/jmaa.2000.7453.

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38

Effros, Edward G., and Zhong-Jin Ruan. "On nonselfadjoint operator algebras." Proceedings of the American Mathematical Society 110, no. 4 (1990): 915. http://dx.doi.org/10.1090/s0002-9939-1990-0986648-8.

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39

Bultheel, A. "Nonselfadjoint operator and related topics." Journal of Computational and Applied Mathematics 66, no. 1-2 (1996): N2—N3. http://dx.doi.org/10.1016/0377-0427(96)80470-5.

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40

Nakamura, Yoshihiro, Kichi-Suke Saito, and Kazunari Sakaba. "The numerical index of nonselfadjoint operator algebras." Proceedings of the American Mathematical Society 117, no. 4 (1993): 1105. http://dx.doi.org/10.1090/s0002-9939-1993-1118086-4.

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41

DUNCAN, BENTON L. "AUTOMORPHISMS OF NONSELFADJOINT DIRECTED GRAPH OPERATOR ALGEBRAS." Journal of the Australian Mathematical Society 87, no. 2 (2009): 175–96. http://dx.doi.org/10.1017/s1446788708081007.

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AbstractWe analyze the automorphism group for the norm closed quiver algebras 𝒯+(Q). We begin by focusing on two normal subgroups of the automorphism group which are characterized by their actions on the maximal ideal space of 𝒯+(Q). To further discuss arbitrary automorphisms we factor automorphism through subalgebras for which the automorphism group can be better understood. This allows us to classify a large number of noninner automorphisms. We suggest a candidate for the group of inner automorphisms.

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42

Sergienko, I. V., A. V. Gladkii, and V. V. Skopetskii. "Simulation of distributed systems with nonselfadjoint operator." Cybernetics and Systems Analysis 30, no. 6 (1994): 830–38. http://dx.doi.org/10.1007/bf02366441.

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43

Mokin, Andrey Yur'evich. "On spectral properties of a nonselfadjoint difference operator." Computer Research and Modeling 2, no. 2 (2010): 143–50. http://dx.doi.org/10.20537/2076-7633-2010-2-2-143-150.

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44

Wogen, W. R. "Counterexamples in the theory of nonselfadjoint operator algebras." Bulletin of the American Mathematical Society 15, no. 2 (1986): 225–28. http://dx.doi.org/10.1090/s0273-0979-1986-15484-4.

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45

Peters, Justin. "The ideal structure of certain nonselfadjoint operator algebras." Transactions of the American Mathematical Society 305, no. 1 (1988): 333. http://dx.doi.org/10.1090/s0002-9947-1988-0920162-6.

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46

Veliev, O. A. "Spectral expansion for a nonselfadjoint periodic differential operator." Russian Journal of Mathematical Physics 13, no. 1 (2006): 101–10. http://dx.doi.org/10.1134/s1061920806010109.

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47

Zolotarev, V. A., and A. A. Yantsevich. "One class of nonlinear operator equations with nonselfadjoint right sides." Journal of Soviet Mathematics 59, no. 1 (1992): 635–38. http://dx.doi.org/10.1007/bf01102484.

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48

Polyakov, D. M. "Spectral analysis of a fourth-order nonselfadjoint operator with nonsmooth coefficients." Siberian Mathematical Journal 56, no. 1 (2015): 138–54. http://dx.doi.org/10.1134/s0037446615010140.

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49

Cheremshantsev, S. E. "EXPANSION IN EIGENFUNCTIONS OF A NONSELFADJOINT OPERATOR WITH PURELY CONTINUOUS SPECTRUM." Mathematics of the USSR-Izvestiya 32, no. 1 (1989): 113–39. http://dx.doi.org/10.1070/im1989v032n01abeh000740.

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50

Roohian, H., and A. I. Shafarevich. "Semiclassical asymptotics of the spectrum of a nonselfadjoint operator on the sphere." Russian Journal of Mathematical Physics 16, no. 2 (2009): 309–14. http://dx.doi.org/10.1134/s1061920809020150.

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