scholarly journals A Study of I-Function of Several Complex Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Prathima Jayarama ◽  
Vasudevan Nambisan Theke Madam ◽  
Shantha Kumari Kurumujji
Keyword(s):  
Natural Generalization ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Generalized Function ◽  
Several Variables ◽  
Special Cases ◽  
Function Of Several Variables ◽  
Function Of Two Variables

The aim of this paper is to introduce a natural generalization of the well-known, interesting, and useful Fox H-function into generalized function of several variables, namely, the I-function of ‘‘r’’ variables. For r=1, we get the I-function introduced and studied by Arjun Rathie (1997) and, for r=2, we get I-function of two variables introduced very recently by ShanthaKumari et al. (2012). Convergent conditions, elementary properties, and special cases have also been given. The results presented in this paper generalize the results of H-function of ‘‘r’’ variables available in the literature.

scholarly journals Geometric Mappings under the Perturbed Extension Operators in Complex Systems Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Chaojun Wang ◽  
Yanyan Cui ◽  
Hao Liu
Keyword(s):  
Complex Systems ◽  
Unit Ball ◽  
Systems Analysis ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Geometric Properties ◽  
Geometric Characteristics ◽  
New Approaches ◽  
Special Cases ◽  
Hartogs Domains

In this paper, we mainly seek conditions on which the geometric properties of subclasses of biholomorphic mappings remain unchanged under the perturbed Roper-Suffridge extension operators. Firstly we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Secondly, applying the analytical characteristics and growth results of subclasses of biholomorphic mappings, we conclude that the generalized Roper-Suffridge operators preserve the geometric properties of strong and almost spiral-like mappings of typeβand orderα,SΩ⁎(β,A,B)as well as almost spiral-like mappings of typeβand orderαunder different conditions on Bergman-Hartogs domains. Sequentially we obtain the conclusions on the unit ballBnand for some special cases. The conclusions include and promote some known results and provide new approaches to construct biholomorphic mappings which have special geometric characteristics in several complex variables.

Remark on Irreducible Factorizations of Polynomials in Several Variables*

1981 ◽  
Vol 24 (4) ◽  
pp. 493-496
Author(s):  
Leiba Rodman
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Analytic Set ◽  
Several Variables ◽  
Set Of Points

AbstractIt is proved that a polynomial on several complex variables, whose coefficients depend analytically on a parameter ε, admits a factorization which is irreducible for every value of the parameter, with the possible exception of an analytic set of points. Moreover, the coefficients of the irreducible factors can be chosen to depend analytically on ε in a neighborhood of every point not belonging to this analytic set.

A theorem of continuation for functions of several complex variables

1958 ◽  
Vol 54 (3) ◽  
pp. 377-382 ◽  
Author(s):  
J. G. Taylor
Keyword(s):  
Field Theory ◽  
Circular Domain ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Quantum Field ◽  
Domain Of Holomorphy ◽  
Envelope Of Holomorphy ◽  
Special Cases ◽  
Theory Of Fields ◽  
Holomorphic Continuation

In the last few years it has been found useful to apply known theorems in the theory of functions of several complex variables to solve problems arising in the quantum theory of fields (11). In particular, in order to derive the dispersion relations of quantum field theory from the general postulates of that theory it appears useful to apply known theorems on holomorphic continuation for functions of several complex variables ((2), (10)). The most important theorems are those which enable a determination to be made of the largest domain to which every function which is holomorphic in a domain D may be continued. This domain is called the envelope of holomorphy of D, and denoted by E(D). If D = E(D) then D is termed a domain of holomorphy. E(D) may be defined as the smallest domain of holomorphy containing D. Only in the special cases that D is a tube, semi-tube, Hartogs, or circular domain has it been possible to determine the envelope of holomorphy E(D) ((3), (7)). An iterative method for the computation of envelopes of holomorphy has recently been given by Bremmerman(4). It is also possible to use the continuity theorem (1) in a direct manner, though in most cases this is exceedingly difficult.

scholarly journals Some Dynamic Inequalities via Diamond Integrals for Function of Several Variables

2021 ◽  
Vol 5 (4) ◽  
pp. 207
Author(s):  
Muhammad Bilal ◽  
Khuram Ali Khan ◽  
Hijaz Ahmad ◽  
Ammara Nosheen ◽  
Khalid Mahmood Awan ◽  
...  
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Jensen’S Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Several Variables ◽  
Time Scale Calculus ◽  
Special Cases ◽  
Function Of Several Variables ◽  
New Inequalities

In this paper, Jensen’s inequality and Fubini’s Theorem are extended for the function of several variables via diamond integrals of time scale calculus. These extensions are used to generalize Hardy-type inequalities with general kernels via diamond integrals for the function of several variables. Some Hardy Hilbert and Polya Knop type inequalities are also discussed as special cases. Classical and new inequalities are deduced from the main results using special kernels and particular time scales.

scholarly journals Some Results of Fekete-Szegö Type. Results for Some Holomorphic Functions of Several Complex Variables

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1707
Author(s):  
Renata Długosz ◽  
Piotr Liczberski
Keyword(s):  
Power Series ◽  
Power Series Expansion ◽  
Holomorphic Functions ◽  
Positive Real Part ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Homogeneous Polynomials ◽  
Positive Real ◽  
Sharp Estimates ◽  
Several Variables

This paper is devoted to a generalization of the well-known Fekete-Szegö type coefficients problem for holomorphic functions of a complex variable onto holomorphic functions of several variables. The considerations concern three families of such functions f, which are bounded, having positive real part and which Temljakov transform Lf has positive real part, respectively. The main result arise some sharp estimates of the Minkowski balance of a combination of 2-homogeneous and the square of 1-homogeneous polynomials occurred in power series expansion of functions from aforementioned families.

scholarly journals Foundations of Fatou Theory and a Tribute to the Work of E. M. Stein on Boundary Behavior of Holomorphic Functions

2021 ◽  
Author(s):  
Fausto Di Biase ◽  
Steven G. Krantz
Keyword(s):  
Harmonic Functions ◽  
Boundary Behavior ◽  
Holomorphic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Several Variables ◽  
The Subject ◽  
Differentiation Of Integrals ◽  
Fatou Theory

AbstractWe lay the foundations of Fatou theory in one and several complex variables. We describe the main contributions contained in E. M. Stein’s book Boundary Behavior of Holomorphic Functions, published in 1972 and still a source of inspiration. We also give an account of his contributions to the study of the boundary behavior of harmonic functions. The point of this paper is not simply to exposit well-known ideas. Rather, we completely reorganize the subject in order to bring out the profound contributions of E. M. Stein to the study of the boundary behavior both of holomorphic and harmonic functions in one and several variables. In an appendix, we provide a self-contained proof of a new result which is relevant to the differentiation of integrals, a topic which, as witnessed in Stein’s work, and especially by the aforementioned book, has deep connections with the boundary behavior of harmonic and holomorphic functions.

scholarly journals Properties of k-beta function with several variables

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Abdur Rehman ◽  
Shahid Mubeen ◽  
Rabia Safdar ◽  
Naeem Sadiq
Keyword(s):  
Beta Function ◽  
Several Variables ◽  
Function Of Several Variables ◽  
Function Of Two Variables

AbstractIn this paper, we discuss some properties of beta function of several variables which are the extension of beta function of two variables. We define k-beta function of several variables and derive some properties of this function which are the extension of k-beta function of two variables, recently defined by Diaz and Pariguan [4]. Also, we extend the formula Γ

scholarly journals An Expansion Theorem Involving H-Function of Several Complex Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Sébastien Gaboury ◽  
Richard Tremblay
Keyword(s):  
Rational Function ◽  
Fractional Derivatives ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Expansion Theorem ◽  
General Expansion ◽  
Special Cases

The aim of this present paper is to obtain a general expansion theorem involving H-functions of several complex variables. This is done by making use of a Taylor-like expansion in terms of a rational function obtained by means of fractional derivatives given recently by the authors. Special cases are also computed.

Advances in Analysis

2014 ◽  
Author(s):  
Charles Fefferman ◽  
Alexandru D. Ionescu ◽  
D.H. Phong ◽  
Stephen Wainger
Keyword(s):  
Fourier Transform ◽  
Representation Theory ◽  
Fourier Analysis ◽  
Interpolation Theorem ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Restriction Theorem ◽  
Several Variables ◽  
Hp Spaces ◽  
The Fourier Transform

Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His fundamental contributions include the Kunze–Stein phenomenon, the construction of new representations, the Stein interpolation theorem, the idea of a restriction theorem for the Fourier transform, and the theory of Hp Spaces in several variables. Through his great discoveries, through books that have set the highest standard for mathematical exposition, and through his influence on his many collaborators and students, Stein has changed mathematics. Drawing inspiration from Stein's contributions to harmonic analysis and related topics, this book gathers papers from internationally renowned mathematicians, many of whom have been Stein's students. The book also includes expository papers on Stein's work and its influence.

THE TUMURA–CLUNIE THEOREM IN SEVERAL COMPLEX VARIABLES

2014 ◽  
Vol 90 (3) ◽  
pp. 444-456 ◽  
Author(s):  
PEI-CHU HU ◽  
CHUNG-CHUN YANG
Keyword(s):  
Meromorphic Function ◽  
Complex Variable ◽  
Nevanlinna Theory ◽  
Meromorphic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Several Variables

AbstractIt is a well-known result that if a nonconstant meromorphic function $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}f$ on $\mathbb{C}$ and its $l$th derivative $f^{(l)}$ have no zeros for some $l\geq 2$, then $f$ is of the form $f(z)=\exp (Az+B)$ or $f(z)=(Az+B)^{-n}$ for some constants $A$, $B$. We extend this result to meromorphic functions of several variables, by first extending the classic Tumura–Clunie theorem for meromorphic functions of one complex variable to that of meromorphic functions of several complex variables using Nevanlinna theory.

Sign in / Sign up

Export Citation Format

Share Document