Convergence of Fourier series on the system of rational functions on the real axis

We consider the systems of rational functions \(\{\Phi_n(z)\}, ~n \in \mathbb{Z}\), defined by fixed set points \({\bf a}:=\{a_k\}_{k=0}^{\infty}, ~ (\mathop{\rm Im} a_k>0)\), \({\bf b}:=\{b_k\}_{k=1}^{\infty}, ~ (\mathop{\rm Im} b_k 1,\) and pointwise convergence of Fourier series on the systems...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2015-07
Main Author: Chaichenko, S O
Format: Article
Language:English
Subjects:
Convergence
Dirichlet problem
Economic impact
Fourier series
Rational functions
Sequences
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider the systems of rational functions \(\{\Phi_n(z)\}, ~n \in \mathbb{Z}\), defined by fixed set points \({\bf a}:=\{a_k\}_{k=0}^{\infty}, ~ (\mathop{\rm Im} a_k>0)\), \({\bf b}:=\{b_k\}_{k=1}^{\infty}, ~ (\mathop{\rm Im} b_k 1,\) and pointwise convergence of Fourier series on the systems \(\{\Phi_n(t)\},~ n \in \mathbb{Z},\) provided that the sequences of poles of these systems satisfies certain restrictions. We have proved statements that are analogues of the classical Theorems of Jordan-Dirichlet and Dini-Lipschitz of convergence of Fourier series on the trigonometric system.
ISSN:2331-8422