LEADER 02568nam 22004455 450 001 9910338256603321 005 20251113195324.0 010 $a3-030-04429-7 024 7 $a10.1007/978-3-030-04429-9 035 $a(CKB)4100000007761804 035 $a(MiAaPQ)EBC5725439 035 $a(DE-He213)978-3-030-04429-9 035 $a(PPN)235231533 035 $a(EXLCZ)994100000007761804 100 $a20190306d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFunctions of Bounded Variation and Their Fourier Transforms /$fby Elijah Liflyand 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019. 215 $a1 online resource (224 pages) 225 1 $aApplied and Numerical Harmonic Analysis,$x2296-5017 311 08$a3-030-04428-9 327 $aStock and tools -- Functions with derivative in a Hardy space -- Integrability spaces: wide, wider and widest -- Sharper results -- Stock and tools for several dimensions -- Integrability of the Fourier transforms -- Sharp results -- Bounded variation and discretization -- Multidimensional case: radial functions. 330 $aFunctions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series. . 410 0$aApplied and Numerical Harmonic Analysis,$x2296-5017 606 $aHarmonic analysis 606 $aAbstract Harmonic Analysis 615 0$aHarmonic analysis. 615 14$aAbstract Harmonic Analysis. 676 $a515.8 676 $a515.8 700 $aLiflyand$b Elijah$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721686 906 $aBOOK 912 $a9910338256603321 996 $aFunctions of Bounded Variation and Their Fourier Transforms$91732485 997 $aUNINA