LEADER 04105nam 2200721 450 001 9910787891703321 005 20230803195202.0 010 $a3-11-026511-7 024 7 $a10.1515/9783110265118 035 $a(CKB)2670000000524191 035 $a(EBL)893608 035 $a(SSID)ssj0001111480 035 $a(PQKBManifestationID)11945061 035 $a(PQKBTitleCode)TC0001111480 035 $a(PQKBWorkID)11130722 035 $a(PQKB)10720871 035 $a(MiAaPQ)EBC893608 035 $a(DE-B1597)172348 035 $a(OCoLC)866853484 035 $a(OCoLC)870589954 035 $a(DE-B1597)9783110265118 035 $a(Au-PeEL)EBL893608 035 $a(CaPaEBR)ebr10838266 035 $a(CaONFJC)MIL574212 035 $a(EXLCZ)992670000000524191 100 $a20131106h20142014 uy| 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aBounded variation and around /$fJu?rgen Appell, Jo?zef Banas?, Nelson Merentes 210 1$aBerlin :$cWalter de Gruyter GmbH & Co. KG,$d[2014] 210 4$dİ2014 215 $a1 online resource (488 p.) 225 0 $aDe Gruyter Series in Nonlinear Analysis and Applications ;$v17 300 $aDescription based upon print version of record. 311 0 $a3-11-026507-9 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$tIntroduction --$t0. Prerequisites --$t1. Classical BV-spaces --$t2. Nonclassical BV-spaces --$t3. Absolutely continuous functions --$t4. Riemann-Stieltjes integrals --$t5. Nonlinear composition operators --$t6. Nonlinear superposition operators --$t7. Some applications --$tReferences --$tList of functions --$tList of symbols --$tIndex --$tBack matter 330 $aThe aim of this monograph is to give a thorough and self-contained account of functions of (generalized) bounded variation, the methods connected with their study, their relations to other important function classes, and their applications to various problems arising in Fourier analysis and nonlinear analysis. In the first part the basic facts about spaces of functions of bounded variation and related spaces are collected, the main ideas which are useful in studying their properties are presented, and a comparison of their importance and suitability for applications is provided, with a particular emphasis on illustrative examples and counterexamples. The second part is concerned with (sometimes quite surprising) properties of nonlinear composition and superposition operators in such spaces. Moreover, relations with Riemann-Stieltjes integrals, convergence tests for Fourier series, and applications to nonlinear integral equations are discussed. The only prerequisite for understanding this book is a modest background in real analysis, functional analysis, and operator theory. It is addressed to non-specialists who want to get an idea of the development of the theory and its applications in the last decades, as well as a glimpse of the diversity of the directions in which current research is moving. Since the authors try to take into account recent results and state several open problems, this book might also be a fruitful source of inspiration for further research. 410 3$aDe Gruyter Series in Nonlinear Analysis and Applications 606 $aFunctions of bounded variation 610 $aBoundary Value Problem. 610 $aBounded Variation. 610 $aContinuity Properties. 610 $aFourier Analysis. 610 $aMonotonicity Properties. 610 $aNonlinear Composition Operators. 610 $aNonlinear Integral Equation. 615 0$aFunctions of bounded variation. 676 $a515/.8 686 $aSK 600$2rvk 700 $aAppell$b Ju?rgen$0350374 701 $aBanas$b Jozef$f1950-$054270 701 $aMerentes$b Nelson$0721518 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910787891703321 996 $aBounded variation and around$91411162 997 $aUNINA