03106nam 2200517 450 99646641260331620230421123325.03-030-74636-410.1007/978-3-030-74636-0(CKB)5590000000486865(DE-He213)978-3-030-74636-0(MiAaPQ)EBC6641045(Au-PeEL)EBL6641045(OCoLC)1257666630(PPN)269152431(EXLCZ)99559000000048686520220205d2021 uy 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierLebesgue points and summability of higher dimensional Fourier series /Ferenc Weisz1st ed. 2021.Cham, Switzerland :Birkhäuser,[2021]©20211 online resource (XIII, 290 p. 24 illus., 1 illus. in color.)3-030-74635-6 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.Summability theorySèries de FourierthubSumabilitatthubLlibres electrònicsthubSummability theory.Sèries de FourierSumabilitat515.243Weisz Ferenc1964-60660MiAaPQMiAaPQMiAaPQBOOK996466412603316Lebesgue Points and Summability of Higher Dimensional Fourier Series2135448UNISA