scholarly journals Relationship Between the Bergman and Cauchy-Szeg¨o Ker- nels in the Domains + (n -1) and ℜn I V

2020 ◽  
pp. 559-567
Author(s):  
Gulmirza Kh. Khudayberganov ◽  
Jonibek Sh. Abdullayev
Keyword(s):  
Holomorphic Functions ◽  
Integral Representations ◽  
Biholomorphic Equivalence

In this paper, a connection has been established between the Bergman and Cauchy-Szeg¨o kernels using the biholomorphic equivalence of the domains + (n -1) and the Lie ball ℜn I V. Moreover, integral representations of holomorphic functions in these domains are obtai

scholarly journals On a Theorem of Bers, with Applications to the Study of Automorphism Groups of Domains

2016 ◽  
Vol 59 (2) ◽  
pp. 346-353
Author(s):  
Steven Krantz
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Holomorphic Functions ◽  
Biholomorphic Equivalence ◽  
Algebras Of Holomorphic Functions

AbstractWe study and generalize a classical theoremof L. Bers that classifies domains up to biholomorphic equivalence in terms of the algebras of holomorphic functions on those domains. Then we develop applications of these results to the study of domains with noncompact automorphism group

scholarly journals Line antiderivations over local fields and their applications

2005 ◽  
Vol 2005 (2) ◽  
pp. 263-309 ◽  
Author(s):  
S. V. Ludkovsky
Keyword(s):  
Laurent Series ◽  
Differential Forms ◽  
Holomorphic Functions ◽  
Integral Representations ◽  
Local Fields ◽  
Cauchy Type ◽  
Series Representations

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential forms such as the Cauchy-Green, Martinelli-Bochner, Leray, Koppelman, and Koppelman-Leray formulas are investigated. Applications to manifold and operator theories are studied.

scholarly journals Stress state of hinged supported thin-wall elastic structures

2021 ◽  
Vol 274 ◽  
pp. 03018
Author(s):  
Lilya Kharasova ◽  
Samat Timergaliev
Keyword(s):  
Boundary Conditions ◽  
Strain State ◽  
Holomorphic Functions ◽  
Integral Representations ◽  
Shell Structures ◽  
Normal Displacement ◽  
Nonlinear Operator Equation ◽  
Stress Strain ◽  
Stress Strain State ◽  
Generalized Displacements

The paper studies the stress-strain state of flat elastic isotropic thin-walled shell structures in the framework of the S. P. Timoshenko shear model with pivotally supported edges. The stress-strain state of shell structures is described by a system of five second-order nonlinear partial differential equations under given static boundary conditions with respect to generalized displacements. The system of equations under study is linear in terms of tangential displacements, rotation angles, and nonlinear in terms of normal displacement. To find a solution to the system that satisfies the given static boundary conditions, integral representations for generalized displacements containing arbitrary holomorphic functions are used. Finding holomorphic functions is one of the main and difficult points in the proposed study. The integral representations constructed in this way allow us to reduce the original problem to a single nonlinear operator equation with respect to the deflection, the solvability of which is established using the principle of compressed maps.

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