Relevant bibliographies by topics / Holomorphic dual-complex functions

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Academic literature on the topic 'Holomorphic dual-complex functions'

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

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

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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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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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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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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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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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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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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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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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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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Book chapters on the topic "Holomorphic dual-complex functions"

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Faraut, Jacques, and Adam Korányi. "Tube Domains Over Convex Cones." In Analysis on Symmetric Cones. Oxford University PressOxford, 1994. http://dx.doi.org/10.1093/oso/9780198534778.003.0009.

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Abstract In this chapter we study complex tube domains over proper convex cones. Our results are ultimately based on the simple fact that the Laplace transform of an integrable function supported in a proper cone defines a holomorphic function in the tube domain over the dual cone. After recalling some basic notions we give a complete exposition of the theory of the Bergman kernel and Bergman metric on general complex domains. Then we proceed to the explicit discussion of the Bergman and Hardy spaces of holomorphic functions on a tube domain over a proper convex cone. We also discuss the Bergm
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Bulnes, Francisco. "Integral Geometry and Cohomology in Field Theory on the Space-Time as Complex Riemannian Manifold." In Advances in Complex Analysis and Applications. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92969.

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The study of the relationships between the integration invariants and the different classes of operators, as well as of functions inside the context of the integral geometry, establishes diverse homologies in the dual space of the functions. This is given in the class of cohomology of the integral operators that give solution to certain class of differential equations in field theory inside a holomorphic context. By this way, using a cohomological theory of appropriate operators that establish equivalences among cycles and cocycles of closed submanifolds, line bundles and contours can be obtai
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