LEADER 04419nam 22007095 450 001 9910279756003321 005 20200704020620.0 010 $a3-319-69808-7 024 7 $a10.1007/978-3-319-69808-3 035 $a(CKB)3840000000347868 035 $a(MiAaPQ)EBC5296109 035 $a(DE-He213)978-3-319-69808-3 035 $a(PPN)224638114 035 $a(EXLCZ)993840000000347868 100 $a20180214d2017 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aAnalysis in Banach Spaces$b[electronic resource] $eVolume II: Probabilistic Methods and Operator Theory /$fby Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (616 pages) $cillustrations, tables 225 1 $aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v67 311 $a3-319-69807-9 320 $aIncludes bibliographical references and index. 327 $a6.Random sums.-7.Type, cotype, and related properties -- 8.R-boundedness -- 9.Square functions and radonifying operators -- 11.The H1-functional calculus -- P.Open problems -- E.Probability theory -- F Banach lattices -- G Semigroups of linear operators -- H.Holomorphic functions on the strip -- I.Muckenhoupt weights -- References -- Index. 330 $aThis second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations. . 410 0$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v67 606 $aFunctional analysis 606 $aOperator theory 606 $aFourier analysis 606 $aPartial differential equations 606 $aProbabilities 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aFunctional analysis. 615 0$aOperator theory. 615 0$aFourier analysis. 615 0$aPartial differential equations. 615 0$aProbabilities. 615 14$aFunctional Analysis. 615 24$aOperator Theory. 615 24$aFourier Analysis. 615 24$aPartial Differential Equations. 615 24$aProbability Theory and Stochastic Processes. 676 $a515.732 700 $aHytönen$b Tuomas$4aut$4http://id.loc.gov/vocabulary/relators/aut$0748040 702 $avan Neerven$b Jan$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVeraar$b Mark$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aWeis$b Lutz$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910279756003321 996 $aAnalysis in Banach Spaces$91989901 997 $aUNINA