國立虎尾科技大學 |

Lebesgue Points and Summability of Higher Dimensional Fourier Series

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Lebesgue Points and Summability of Higher Dimensional Fourier Series/ by Ferenc Weisz.
Author:	Weisz, Ferenc.
Description:	XIII, 290 p. 24 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Fourier analysis. -
Online resource:	https://doi.org/10.1007/978-3-030-74636-0
ISBN:	9783030746360

Lebesgue Points and Summability of Higher Dimensional Fourier Series
Weisz, Ferenc.

Lebesgue Points and Summability of Higher Dimensional Fourier Series[electronic resource] /by Ferenc Weisz. - 1st ed. 2021. - XIII, 290 p. 24 illus., 1 illus. in color.online resource.

One-dimensional Fourier series -- lq-summability of higher dimensional Fourier series -- Rectangular summability of higher dimensional Fourier series -- Lebesgue points of higher dimensional functions.

This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.

ISBN: 9783030746360

Standard No.: 10.1007/978-3-030-74636-0doiSubjects--Topical Terms:

639284
Fourier analysis.

LC Class. No.: QA403.5-404.5

Dewey Class. No.: 515.2433

Lebesgue Points and Summability of Higher Dimensional Fourier Series
LDR:02968nam a22003975i 4500 001 1055451
003 DE-He213
005 20210618115416.0
007 cr nn 008mamaa
008 220103s2021 gw | s |||| 0|eng d
020 $a 9783030746360 $9 978-3-030-74636-0
024 7 $a 10.1007/978-3-030-74636-0 $2 doi
035 $a 978-3-030-74636-0
050 4 $a QA403.5-404.5
072 7 $a PBKF $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.2433 $2 23
100 1 $a Weisz, Ferenc. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1198024
245 1 0 $a Lebesgue Points and Summability of Higher Dimensional Fourier Series $h [electronic resource] / $c by Ferenc Weisz.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2021.
300 $a XIII, 290 p. 24 illus., 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a One-dimensional Fourier series -- lq-summability of higher dimensional Fourier series -- Rectangular summability of higher dimensional Fourier series -- Lebesgue points of higher dimensional functions.
520 $a This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.
650 0 $a Fourier analysis. $3 639284
650 0 $a Sequences (Mathematics). $3 1253882
650 0 $a Measure theory. $3 527848
650 1 4 $a Fourier Analysis. $3 672627
650 2 4 $a Sequences, Series, Summability. $3 672022
650 2 4 $a Measure and Integration. $3 672015
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030746353
776 0 8 $i Printed edition: $z 9783030746377
776 0 8 $i Printed edition: $z 9783030746384
856 4 0 $u https://doi.org/10.1007/978-3-030-74636-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)