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Journal articles on the topic 'Holomorphic dual-complex functions'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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1

Khoryakova, Yulia Alexandrovna, and Aleksandr Anatol'evich Shlapunov. "On Grothendieck-type duality for spaces of holomorphic functions of several variables." Sbornik: Mathematics 215, no. 8 (2024): 1114–33. http://dx.doi.org/10.4213/sm9956e.

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We describe the strong dual space $({\mathcal O} (D))^*$ of the space ${\mathcal O} (D)$ of holomorphic functions of several complex variables in a bounded domain $D$ with Lipschitz boundary and connected complement (as usual, ${\mathcal O} (D)$ is endowed with the topology of local uniform convergence in $D$). We identify the dual space with the closed subspace of the space of harmonic functions on the closed set ${\mathbb C}^n\setminus D$, $n>1$, whose elements vanish at the point at infinity and satisfy the Cauchy-Riemann tangential conditions on $\partial D$. In particular, we generaliz
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2

DRIVER, BRUCE K., LEONARD GROSS, and LAURENT SALOFF-COSTE. "Surjectivity of the Taylor map for complex nilpotent Lie groups." Mathematical Proceedings of the Cambridge Philosophical Society 146, no. 1 (2009): 177–95. http://dx.doi.org/10.1017/s0305004108001692.

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AbstractA Hermitian formqon the dual space,*, of the Lie algebra,, of a simply connected complex Lie group,G, determines a sub-Laplacian, Δ, onG. Assuming Hörmander's condition for hypoellipticity, there is a smooth heat kernel measure, ρt, onGassociated toetΔ/4. In a companion paper [6], we proved the existence of a unitary “Taylor” map from the space of holomorphic functions inL2(G, ρt) ontoJt0(a subspace of) the dual of the universal enveloping algebra of. Here we give a very different proof of the surjectivity of the Taylor map under the assumption thatGis nilpotent. This proof provides fu
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3

Meštrović, Romeo. "Topological and Functional Properties of SomeF-Algebras of Holomorphic Functions." Journal of Function Spaces 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/850709.

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LetNp (1<p<∞)be the Privalov class of holomorphic functions on the open unit diskDin the complex plane. The spaceNpequipped with the topology given by the metricdpdefined bydp(f,g)=(∫02π‍(log(1+|f∗(eiθ)-g∗(eiθ)|))p(dθ/2π))1/p,f,g∈Np, becomes anF-algebra. For eachp>1, we also consider the countably normed Fréchet algebraFpof holomorphic functions onDwhich is the Fréchet envelope of the spaceNp. Notice that the spacesFpandNphave the same topological duals. In this paper, we give a characterization of bounded subsets of the spacesFpand weakly bounded subsets of the spacesNpwithp>1. If
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4

Aristov, O. Yu. "On holomorphic reflexivity conditions for complex Lie groups." Proceedings of the Edinburgh Mathematical Society 64, no. 4 (2021): 800–821. http://dx.doi.org/10.1017/s0013091521000572.

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AbstractWe consider Akbarov's holomorphic version of the non-commutative Pontryagin duality for a complex Lie group. We prove, under the assumption that $G$ is a Stein group with finitely many components, that (1) the topological Hopf algebra of holomorphic functions on $G$ is holomorphically reflexive if and only if $G$ is linear; (2) the dual cocommutative topological Hopf algebra of exponential analytic functional on $G$ is holomorphically reflexive. We give a counterexample, which shows that the first criterion cannot be extended to the case of infinitely many components. Nevertheless, we
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5

DECK, THOMAS. "HIDA DISTRIBUTIONS ON COMPACT LIE GROUPS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 03, no. 03 (2000): 337–62. http://dx.doi.org/10.1142/s0219025700000224.

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We show that a nuclear space of analytic functions on K is associated with each compact, connected Lie group K. Its dual space consists of distributions (generalized functions on K) which correspond to the Hida distributions in white noise analysis. We extend Hall's transform to the space of Hida distributions on K. This extension — the S-transform on K — is then used to characterize Hida distributions by holomorphic functions satisfying exponential growth conditions (U-functions). We also give a tensor description of Hida distributions which is induced by the Taylor map on U-functions. Finall
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Kudasheva, Elena Gennad'evna, Enzhe Bulatovna Menshikova, and Bulat Nurmievich Khabibullin. "Dual construction and existence of (pluri)subharmonic minorant." Ufa Mathematical Journal 16, no. 3 (2024): 65–73. https://doi.org/10.13108/2024-16-3-65.

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We study the existence and construction of subharmonic or plurisubharmonic function enveloping from below a function on a subset in finite - dimensional real or complex space. These problems naturally arise in theories of uniform algebras, potential and complex potential, which was reflected in works by D.A. Edwards, T.V. Gamelin, E.A. Poletsky, S. Bu and W. Schachermayer, B.J. Cole and T.J. Ransford, F. Lárusson and S. Sigurdsson and many others. In works in 1990s and recently we showed that these problems play a key role in studying nontriviality of weighted spaces of holomorphic
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7

DUMITRESCU, Horia, Vladimir CARDOS, and Radu BOGATEANU. "The Euler’s harmonic holomorphic regenerative universe." INCAS BULLETIN 16, no. 1 (2024): 45–58. http://dx.doi.org/10.13111/2066-8201.2024.16.1.5.

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The Cartesian dualism is a precursor to Euler’s complex theory, that completes the Descartes-Leibnitz monadic conception using the natural quanta (non-splitting e, π) along with their topological torsion in the form of dual isomorphism. The complete Euler’s identity controls a bounded regenerative/ recurrent multiverse (a kind of multigraph) by two regenerative exponential functions, one quantic, e = exp (1) and another gravitational, g0 ≡ 10 = exp (1) with the fixed points, g0 = π2 and (g0g0) respectively. Physically, the fixed points give the well-defined the unit gravity (g0 m/s2) and light
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8

Khabibullin, B. N. "Subharmonic envelopes for functions on domains." Vestnik of Samara University. Natural Science Series 29, no. 3 (2023): 64–71. http://dx.doi.org/10.18287/2541-7525-2023-29-3-64-71.

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One of the most common problems in various fields of real and complex analysis is the questions of the existence and construction for a given function of an envelope from below or from above of a function from a special class H. We consider a case when H is the convex cone of all subharmonic functions on the domain D of a finite-dimensional Euclidean space over the field of real numbers. For a pair of subharmonic functions u and M from this convex cone H, dual necessary and sufficient conditions are established under which there is a subharmonic function h ̸≡ −∞, “dampening the growth” of the
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9

BISWAS, INDRANIL, JACQUES HURTUBISE, and A. K. RAINA. "RANK ONE CONNECTIONS ON ABELIAN VARIETIES." International Journal of Mathematics 22, no. 11 (2011): 1529–43. http://dx.doi.org/10.1142/s0129167x11007318.

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Let A be a complex abelian variety. The moduli space [Formula: see text] of rank one algebraic connections on A is a principal bundle over the dual abelian variety A∨ = Pic 0(A) for the group [Formula: see text]. Take any line bundle L on A∨; let [Formula: see text] be the algebraic principal [Formula: see text]-bundle over A∨ given by the sheaf of connections on L. The line bundle L produces a homomorphism [Formula: see text]. We prove that [Formula: see text] is isomorphic to the principal [Formula: see text]-bundle obtained by extending the structure group of the principal [Formula: see tex
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10

SAYGILI, K. "TOPOLOGICALLY MASSIVE ABELIAN GAUGE THEORY." International Journal of Modern Physics A 23, no. 13 (2008): 2015–35. http://dx.doi.org/10.1142/s0217751x08039840.

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We discuss three mathematical structures which arise in topologically massive Abelian gauge theory. First, the Euclidean topologically massive Abelian gauge theory defines a contact structure on a manifold. We briefly discuss three solutions and the related contact structures on the flat 3-torus, the AdS space, the 3-sphere which respectively correspond to Bianchi type I, VIII, IX spaces. We also present solutions on Bianchi type II, VI and VII spaces. Secondly, we discuss a family of complex (anti-)self-dual solutions of the Euclidean theory in Cartesian coordinates on [Formula: see text] whi
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11

FARID, MESSELMI. "DUAL-COMPLEX NUMBERS AND THEIR HOLOMORPHIC FUNCTIONS." August 5, 2013. https://doi.org/10.5281/zenodo.22961.

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The purpose of this paper is to contribute to development a general theory of dual-complex numbers. We start by de ne the notion of dual- complex and their algebraic properties. In addition, we develop a simple mathematical method based on matrices, simplifying manipulation of dual-complex numbers. Inspired from complex analysis, we generalize the concept of holomorphicity to dual-complex functions. Moreover, a general representation of holomorphic dual-complex functions has been obtained. Finally and as concrete examples, some usual complex functions have been generalized to th
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12

Colombo, Fabrizio, Antonino De Martino, Kamal Diki, Irene Sabadini, and Daniele C. Struppa. "Duality theorems for polyanalytic functions." Forum Mathematicum, February 10, 2025. https://doi.org/10.1515/forum-2024-0022.

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Abstract The goal of this paper is to give a characterization of the dual of the space of polyanalytic functions on the complement of a compact set K and vanishing at infinity. The class of polyanalytic functions generalizes holomorphic functions and serves as a middle ground between holomorphic functions in one complex variable and those in two complex variables. The duality result is also expressed in topological terms through a new class of infinite-order differential operators, which includes well-known families of operators like the Laplace and Helmholtz operators. Since the notion of pol
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13

Aron, Richard, Verónica Dimant, Luis C. García‐Lirola, and Manuel Maestre. "Linearization of holomorphic Lipschitz functions." Mathematische Nachrichten, May 3, 2024. http://dx.doi.org/10.1002/mana.202300527.

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AbstractLet and be complex Banach spaces with denoting the open unit ball of . This paper studies various aspects of the holomorphic Lipschitz space , endowed with the Lipschitz norm. This space consists of the functions in the intersection of the sets of Lipschitz mappings and of bounded holomorphic mappings, from to . Thanks to the Dixmier–Ng theorem, is indeed a dual space, whose predual shares linearization properties with both the Lipschitz‐free space and Dineen–Mujica predual of . We explore the similarities and differences between these spaces, and combine techniques to study the proper
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14

Gupta, Varun. "Holographic M5 branes in AdS7 × S4." Journal of High Energy Physics 2021, no. 12 (2021). http://dx.doi.org/10.1007/jhep12(2021)032.

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Abstract We study classical M5 brane solutions in the probe limit in the AdS7× S4 background geometry that preserve the minimal amount of supersymmetry. These solutions describe the holography of codimension-2 defects in the 6d boundary dual $$ \mathcal{N} $$ N = (0, 2) supersymmetric gauge theories. The general solution is described in terms of holomorphic functions that satisfy a scaling condition. We show the behavior of the world-volume of a special class of BPS solutions near the AdS boundary region can be characterized by general equations, which describe it as intersections of the zeros
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15

Robson, C. J. "Self-Dual Maxwell Fields from Clifford Analysis." Advances in Applied Clifford Algebras 35, no. 1 (2024). https://doi.org/10.1007/s00006-024-01368-1.

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AbstractThe study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher dimensions. In this paper, I decompose the Cauchy-Riemann equations for a general Clifford algebra into grades using the Geometric Algebra formalism, and show that for the Spacetime Algebra Cl(3, 1) these equations are the equations for a self-dual source free Maxwell field, and for a massless uncharged Spinor. This shows a deep link between fundamental phy
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16

Chattopadhyaya, Aradhita, Jan Manschot, and Swapnamay Mondal. "Scaling black holes and modularity." Journal of High Energy Physics 2022, no. 3 (2022). http://dx.doi.org/10.1007/jhep03(2022)001.

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Abstract Scaling black holes are solutions of supergravity with multiple black hole singularities, which can be adiabatically connected to a single center black hole solution. We develop techniques to determine partition functions for such scaling black holes, if each constituent carries a non-vanishing magnetic charge corresponding to a D4-brane in string theory, or equivalently M5-brane in M-theory. For three constituents, we demonstrate that the partition function is a mock modular form of depth two, and we determine the appropriate non-holomorphic completion using generalized error functio
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17

Adamo, Tim, Giuseppe Bogna, Lionel Mason, and Atul Sharma. "Gluon scattering on the self-dual dyon." Letters in Mathematical Physics 115, no. 1 (2025). https://doi.org/10.1007/s11005-025-01907-2.

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Abstract The computation of scattering amplitudes in the presence of non-trivial background gauge fields is an important but extremely difficult problem in quantum field theory. In even the simplest backgrounds, obtaining explicit formulae for processes involving more than a few external particles is often intractable. Recently, it has been shown that remarkable progress can be made by considering background fields which are chiral in nature. In this paper, we obtain a compact expression for the tree-level, maximal helicity violating (MHV) scattering amplitude of an arbitrary number of gluons
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18

Ashok, Sujay K., Varun Gupta, and Nemani V. Suryanarayana. "On BPS strings in $$ \mathcal{N} $$ = 4 Yang-Mills theory." Journal of High Energy Physics 2021, no. 1 (2021). http://dx.doi.org/10.1007/jhep01(2021)008.

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Abstract We study singular time-dependent $$ \frac{1}{8} $$ 1 8 -BPS configurations in the abelian sector of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory that represent BPS string-like defects in ℝ × S3 spacetime. Such BPS strings can be described as intersections of the zeros of holomorphic functions in two complex variables with a 3-sphere. We argue that these BPS strings map to $$ \frac{1}{8} $$ 1 8 -BPS surface operators under the state-operator correspondence of the CFT. We show that the string defects are holographically dual to noncompact probe D3-branes in global AdS5 × S5
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19

Geuchen, Paul, Thomas Jahn, and Hannes Matt. "Universal approximation with complex-valued deep narrow neural networks." Constructive Approximation, June 1, 2025. https://doi.org/10.1007/s00365-025-09713-8.

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Abstract We study the universality of complex-valued neural networks with bounded widths and arbitrary depths. Under mild assumptions, we give a full description of those activation functions $$\varrho :\mathbb {C}\rightarrow \mathbb {C}$$ ϱ : C → C that have the property that their associated networks are universal, i.e., are capable of approximating continuous functions to arbitrary accuracy on compact domains. Precisely, we show that deep narrow complex-valued networks are universal if and only if their activation function is neither holomorphic, nor antiholomorphic, nor $$\mathbb {R}$$ R -
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20

Mayerson, Daniel R., Robert A. Walker, and Nicholas P. Warner. "Microstate geometries from gauged supergravity in three dimensions." Journal of High Energy Physics 2020, no. 10 (2020). http://dx.doi.org/10.1007/jhep10(2020)030.

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Abstract The most detailed constructions of microstate geometries, and particularly of superstrata, are done using $$ \mathcal{N} $$ N = (1, 0) supergravity coupled to two anti-self-dual tensor multiplets in six dimensions. We show that an important sub-sector of this theory has a consistent truncation to a particular gauged supergravity in three dimensions. Our consistent truncation is closely related to those recently laid out by Samtleben and Sarıoğlu [1], which enables us to develop complete uplift formulae from the three-dimensional theory to six dimensions. We also find a new family of m
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21

Emmerson, Parker. "Quasi-Quanta Language Package." July 18, 2023. https://doi.org/10.5281/zenodo.8157754.

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I investigate combinations of quasi-quanta expressions and how they yield alternate solutions for expressions in Morphic Topology of Numeric Energy: A Fractal Morphism of Topological Counting Shows Real Differentiation of Numeric Energy.   For Praising Jehovah, I do publish these mathematical gesturing forms from the infinity meaning of His word. Thanks mom! This quasi-quanta language package outlines methods for combining by topo- logical functor entanglement, symbolic, numeric-energy components. Methods, guidelines and algebraic rules for combining the quasi-quanta into t
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