LEADER 04841nam 22007215 450 001 9910300248803321 005 20250717140245.0 010 $a94-6239-163-7 024 7 $a10.2991/978-94-6239-163-5 035 $a(CKB)3710000000541915 035 $a(EBL)4305881 035 $a(SSID)ssj0001597230 035 $a(PQKBManifestationID)16297053 035 $a(PQKBTitleCode)TC0001597230 035 $a(PQKBWorkID)14885835 035 $a(PQKB)11311603 035 $a(DE-He213)978-94-6239-163-5 035 $a(MiAaPQ)EBC4305881 035 $z(PPN)258862459 035 $a(PPN)190882808 035 $a(EXLCZ)993710000000541915 100 $a20151229d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations $eA Monograph Based on Articles of the Founding Authors, Reproduced in Full /$fby Radomir Stankovic, Paul Leo Butzer, Ferenc Schipp, William R. Wade, Weiyi Su, Yasushi Endow, Sandor Fridli, Boris I. Golubov, Franz Pichler 205 $a1st ed. 2015. 210 1$aParis :$cAtlantis Press :$cImprint: Atlantis Press,$d2015. 215 $a1 online resource (370 p.) 225 1 $aAtlantis Studies in Mathematics for Engineering and Science,$x2467-9631 ;$v13 300 $aDescription based upon print version of record. 311 08$a94-6239-162-9 320 $aIncludes bibliographical references and index. 327 $aEarly Work in Gibbs Differentiation in China -- Gibbs-Butzer Calculus and Pseudo-differential Operators on Local Fields -- Early Work in Gibbs Differentiation in Soviet Union ? SSSR -- Research in Dyadic Differentiation in Russia -- Generalized Derivatives and Integrals on Vilenkin Groups -- Calculus on Walsh and Vilenkin Groups -- Gibbs Derivatives on Groups -- My Research in Gibbs Derivatives on Finite Groups -- Ef?cient Computation of Gibbs Derivatives on Finite Abelian Groups -- Gibbs Derivative and Walsh Harmonizable DSP -- My Involvement in Gibbs Derivatives and Walsh Harmonizable Processes -- Open Problems in Theory and Applications of Dyadic Derivatives. 330 $aThe second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory.  Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area. 410 0$aAtlantis Studies in Mathematics for Engineering and Science,$x2467-9631 ;$v13 606 $aHarmonic analysis 606 $aComputer science$xMathematics 606 $aAbstract Harmonic Analysis 606 $aMathematical Applications in Computer Science 615 0$aHarmonic analysis. 615 0$aComputer science$xMathematics. 615 14$aAbstract Harmonic Analysis. 615 24$aMathematical Applications in Computer Science. 676 $a510 700 $aStankovic?$b Radomir S.$4aut$4http://id.loc.gov/vocabulary/relators/aut$00 702 $aButzer$b Paul Leo$f1928-$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSchipp$b F$g(Ferenc),$f1939-$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aWade$b William R.$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSu$b Weiyi$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aEndow$b Yasushi$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aFridli$b Sandor$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aGolubov$b B. I$g(Boris Ivanovich),$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPichler$b Franz$f1936-$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300248803321 996 $aDyadic Walsh analysis from 1924 onwards Walsh-Gibbs-Butzer dyadic differentiation in science volume 2 extensions and generalizations$94157879 997 $aUNINA