Matrix transformations of sequences and applications in Fourier analysis

Ushangi Goginava; Sawsan Omira; Reem Abdel-Latif; Tasnem AlKrinat

doi:10.1016/j.heliyon.2024.e29585

Matrix transformations of sequences and applications in Fourier analysis

Ushangi Goginava, Sawsan Omira, Reem Abdel-Latif, Tasnem AlKrinat

Research output: Contribution to journal › Article › peer-review

Abstract

In the presented paper we consider a sequence and its Nörlud and a generalized mean derived from a matrix transformation. Furthermore, sufficient conditions for the matrix are found which implies the converges of the generalized matrix means from the Nörlud ones. The results drawn make it possible to transfer well-known theorems in the theory of Fourier series to more general sequences of operators.

Original language	English
Article number	e29585
Journal	Heliyon
Volume	10
Issue number	8
DOIs	https://doi.org/10.1016/j.heliyon.2024.e29585
Publication status	Published - Apr 30 2024

Keywords

Almost everywhere convergence
Matrix transformation
Numerical sequences
Trigonometric system
Vilenkin system
Walsh-Kaczmarz system
Walsh-Paley system

ASJC Scopus subject areas

General

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10.1016/j.heliyon.2024.e29585

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abstract = "In the presented paper we consider a sequence and its N{\"o}rlud and a generalized mean derived from a matrix transformation. Furthermore, sufficient conditions for the matrix are found which implies the converges of the generalized matrix means from the N{\"o}rlud ones. The results drawn make it possible to transfer well-known theorems in the theory of Fourier series to more general sequences of operators.",

keywords = "Almost everywhere convergence, Matrix transformation, Numerical sequences, Trigonometric system, Vilenkin system, Walsh-Kaczmarz system, Walsh-Paley system",

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AU - Goginava, Ushangi

AU - Omira, Sawsan

AU - Abdel-Latif, Reem

AU - AlKrinat, Tasnem

PY - 2024/4/30

Y1 - 2024/4/30

N2 - In the presented paper we consider a sequence and its Nörlud and a generalized mean derived from a matrix transformation. Furthermore, sufficient conditions for the matrix are found which implies the converges of the generalized matrix means from the Nörlud ones. The results drawn make it possible to transfer well-known theorems in the theory of Fourier series to more general sequences of operators.

AB - In the presented paper we consider a sequence and its Nörlud and a generalized mean derived from a matrix transformation. Furthermore, sufficient conditions for the matrix are found which implies the converges of the generalized matrix means from the Nörlud ones. The results drawn make it possible to transfer well-known theorems in the theory of Fourier series to more general sequences of operators.

KW - Almost everywhere convergence

KW - Matrix transformation

KW - Numerical sequences

KW - Trigonometric system

KW - Vilenkin system

KW - Walsh-Kaczmarz system

KW - Walsh-Paley system

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JO - Heliyon

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Matrix transformations of sequences and applications in Fourier analysis

Abstract

Keywords

ASJC Scopus subject areas

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