Holomorphic functions

Continued part 1, part 2 of ebook "Holomorphic functions and integral representations in several complex variables" provides readers with contents including: the levi problem and the solution of δ on strictly pseudoconvex domains; function theory on domains of holomorphy in Cn; topics in function theory on strictly pseudoconvex domains;...

198p lytamnguyet 04-08-2023 10 4   Download

Part 1 of ebook "Mathematical methods in Physics: Distributions, Hilbert space operators, variational methods, and applications in quantum physics" provides readers with contents including: spaces of test functions; schwartz distributions; calculus for distributions; distributions as derivatives of functions; tensor products; convolution products; applications of convolution; holomorphic functions; fourier transformation; distributions as boundary values of analytic functions;...

217p lytamnguyet 04-08-2023 7 4   Download

Part 1 of ebook "Holomorphic functions and integral representations in several complex variables" provides readers with contents including: elementary local properties of holomorphic functions; domains of holomorphy and pseudoconvexity; differential forms and hermitian geometry; integral representations in Cn;...

206p lytamnguyet 04-08-2023 3 3   Download

In the note "Some results relate to the maximum principle of the subharmonic functions on the unit disc", we apply the maximum principle of subharmonic functions on the complex plane to prove some results related to the holomorphic functions and the subharmonic functions on unit disc in the complex plane.

6p nhanchienthien 25-07-2023 8 4   Download

In this paper, we clarify some throughout examples, and we also show the equivalence between the complex version of Rolle's theorem and Lagrangle’s mean value theorem.

7p viharry 15-12-2022 5 2   Download

The purpose of this paper "Linear topological invariants of spaces of holomorphic functions in infinite dimension" is to investigate the existence of generalized solutions for strongly parabolic systems in a cylindrical domain. The decay of the solution at infinity, depending on the right-hand of the equation, is also studied in this article.

18p runordie5 04-07-2022 6 1   Download

The relation between weak extensibility and extensibility of vector-valued holomorphic functions on open sets and on compact sets has been investigated by many authors, for example Ligocka and Siciak for open sets in a metric vector space, Siciakand Waelbroeck for compact sets in \({{C^n}}\), N. V. Khue and B. D. Tac for compact sets in a nuclear metric vector space. The aim of the present note is to prove some results for Banach-valued meromorphic functions on open sets and on compact sets in \({{C^n}}\).

6p runordie5 04-07-2022 22 3   Download

The aim of the paper "The non-pluripolarity of compact sets in complex spaces and the property \((L{B^\infty })\) for the space of germs of holomorphic functions" is to establish the equivalence between the nonpluripolarity of a compact set in a complex space and the property \((L{B^\infty })\) for the dual space of the space of germs of holomorphic functions on that compact set.

12p runordie5 04-07-2022 8 2   Download

In the note "Weak Runge pairs in \({C^n}\)", the authors give a characterization for a pair of pseudoconvex domains in \({C^n}\), (D', D), D' \( \subset \) D such that holomorphic functions on D' can be approximated uniformly on compact sets by meromorphic function on D. Explicit examples are also given.

8p runordie5 04-07-2022 8 2   Download

Let D be a domain in C n . We introduce a class of pluripolar sets in D which is essentially contained in the class of complete pluripolar sets. An application of this new class to the problem of approximation of holomorphic functions is also given.

17p runordie3 27-06-2022 6 3   Download

Value distribution theory for holomorphic curves which also known as Nevanlinna-Cartan theory was originated by the work of H. Cartan in 1933. Since that time, it had attracted the attention of many mathematicians and had many important publications and it had many applications in different areas of mathematics.

8p vimarissamayer 02-06-2022 10 3   Download

We show that the analogue of Mason Theorem for p-adic entire function in several variables is true. The following will be discussed in this paper: Height of p−adic holomorphic functions of several variables, Height of p−adic meromorphic functions of several variables.

10p tradaviahe12 06-01-2021 15 1   Download

In this article, we prove some normality criteria for a family of meromorphic functions, which involves sharing of a nonzero value by certain differential monomials generated by the members of the family. These results generalize some of the results of Schwick.

16p danhdanh27 07-01-2019 17 1   Download

In this article we generalized some properties of Banach algebras, to a new class of topological algebras namely fundamental and fundamental locally multiplicative topological algebras (abbreviated by F LM ). Also the new notion of sub-multiplicatively metrizable topological algebra is given and some well known spectral properties of Banach algebras are generalized to such kind of algebras.

7p tuongvidanh 06-01-2019 30 1   Download

We clearly do not investigate the conditions under which there are continuous solution in G even when the boundary vector family has positive index. In this work, the classical Riemann Hilbert boundary value problem is extended to generalized Q-holomorphic functions.

14p tuongvidanh 06-01-2019 11 1   Download

In this paper, by using the second main theorem for holomorphic curves from annuli ∆ to P n(C) intersecting a collection of fixed hyperplanes in general position with truncated counting functions, we will prove some theorems on unicity for linearly non-degenerate holomorphic curves on annulus ignoring multiplicity with hyperplanes in general position in projective space. This theorems have shown the sufficient conditions for two linearly non-degenerate holomorphic curves being equivalent.

7p doctorstrange1 21-06-2018 25 2   Download

The purpose of this paper is to carry out the abelianization program proposed by Atiyah [1] and Hitchin [9] for the geometric quantization of SU(2) Wess-Zumino-Witten model. Let C be a Riemann surface of genus g. Let Mg be the moduli space of semi-stable rank 2 holomorphic vector bundles on C with trivial determinant. For a positive integer k, let Γ(Mg , Lk ) be the space of holomorphic sections of the k-th tensor product of the determinant line bundle L on Mg . An element of Γ(Mg , Lk ) is called a rank 2 theta function...

50p noel_noel 17-01-2013 59 8   Download

To Bidisha and Ananya Abstract We prove integrality of the ratio f, f / g, g (outside an explicit finite set of primes), where g is an arithmetically normalized holomorphic newform on a Shimura curve, f is a normalized Hecke eigenform on GL(2) with the same Hecke eigenvalues as g and , denotes the Petersson inner product. The primes dividing this ratio are shown to be closely related to certain level-lowering congruences satisfied by f and to the central values of a family of Rankin-Selberg L-functions. Finally we give two applications, the first to proving the integrality of a...

68p noel_noel 17-01-2013 53 6   Download

Let G be a connected, real, semisimple Lie group contained in its complexification GC , and let K be a maximal compact subgroup of G. We construct a KC -G double coset domain in GC , and we show that the action of G on the K-finite vectors of any irreducible unitary representation of G has a holomorphic extension to this domain. For the resultant holomorphic extension of K-finite matrix coefficients we obtain estimates of the singularities at the boundary, as well as majorant/minorant estimates along the boundary. ...

85p tuanloccuoi 04-01-2013 47 7   Download

A basic result in the theory of holomorphic functions of several complex variables is the following special case of the work of H. Cartan on the sheaf cohomology on Stein domains ([10], or see [14] or [16] for more modern treatments). Theorem 1.1. If V is an analytic variety in a domain of holomorphy Ω and if f is a holomorphic function on V , then there is a holomorphic function g in Ω such that g = f on V . The subject of this paper concerns an add-on to the structure considered in Theorem 1.1 which...

25p tuanloccuoi 04-01-2013 50 5   Download