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010   $a3-030-74636-4
024 7 $a10.1007/978-3-030-74636-0
035   $a(CKB)5590000000486865
035   $a(DE-He213)978-3-030-74636-0
035   $a(MiAaPQ)EBC6641045
035   $a(Au-PeEL)EBL6641045
035   $a(OCoLC)1257666630
035   $a(PPN)269152431
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100   $a20220205d2021      uy             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aLebesgue points and summability of higher dimensional Fourier series /$fFerenc Weisz
205   $a1st ed. 2021.
210  1$aCham, Switzerland :$cBirkha?user,$d[2021]
210  4$d©2021
215   $a1 online resource (XIII, 290 p. 24 illus., 1 illus. in color.)
311   $a3-030-74635-6 
327   $aOne-dimensional Fourier series -- lq-summability of higher dimensional Fourier series -- Rectangular summability of higher dimensional Fourier series -- Lebesgue points of higher dimensional functions.
330   $aThis 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.
606   $aSummability theory
606   $aSèries de Fourier$2thub
606   $aSumabilitat$2thub
608   $aLlibres electrònics$2thub
615  0$aSummability theory.
615  7$aSèries de Fourier
615  7$aSumabilitat
676   $a515.243
700   $aWeisz$b Ferenc$f1964-$060660
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466412603316
996   $aLebesgue Points and Summability of Higher Dimensional Fourier Series$92135448
997   $aUNISA