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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aResearch Topics in Analysis, Volume I$b[electronic resource] $eGrounding Theory /$fby Shouchuan Hu, Nikolaos S. Papageorgiou
205   $a1st ed. 2022.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2022.
215   $a1 online resource (544 pages)
225 1 $aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894
311 08$aPrint version: Hu, Shouchuan Research Topics in Analysis, Volume I Cham : Springer International Publishing AG,c2022 9783031178368 
320   $aIncludes bibliographical references and index.
327   $aVolume I - Theory: - Topology -- Measure Theory -- Banach Space Theory -- Function Spaces -- Multivalued Analysis -- Smooth and Nonsmooth Calculus -- Nonlinear Operators -- Variational Analysis -- References.
330   $aThis book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed. Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems ? handy for understanding and self-study ? and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume. By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
410  0$aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894
606   $aFunctional analysis
606   $aTopology
606   $aMathematical optimization
606   $aCalculus of variations
606   $aFunctional Analysis
606   $aTopology
606   $aCalculus of Variations and Optimization
606   $aAnàlisi funcional$2thub
606   $aAnàlisi matemàtica$2thub
608   $aLlibres electrònics$2thub
615  0$aFunctional analysis.
615  0$aTopology.
615  0$aMathematical optimization.
615  0$aCalculus of variations.
615 14$aFunctional Analysis.
615 24$aTopology.
615 24$aCalculus of Variations and Optimization.
615  7$aAnàlisi funcional
615  7$aAnàlisi matemàtica
676   $a515.7
700   $aHu$b Shouchuan$0730634
702   $aPapageorgiou$b Nikolaos S.
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910633910403321
996   $aResearch Topics in Analysis, Volume I$93562122
997   $aUNINA