LEADER 04074nam 22006255 450 001 9910484421903321 005 20200705103734.0 010 $a1-0716-0332-9 024 7 $a10.1007/978-1-0716-0332-1 035 $a(CKB)4100000010480176 035 $a(DE-He213)978-1-0716-0332-1 035 $a(MiAaPQ)EBC6120128 035 $a(PPN)242977073 035 $a(EXLCZ)994100000010480176 100 $a20200222d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aModulation Spaces$b[electronic resource] $eWith Applications to Pseudodifferential Operators and Nonlinear Schrödinger Equations /$fby Árpád Bényi, Kasso A. Okoudjou 205 $a1st ed. 2020. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2020. 215 $a1 online resource (XVI, 169 p. 3 illus.) 225 1 $aApplied and Numerical Harmonic Analysis,$x2296-5009 311 $a1-0716-0330-2 327 $aNotions of real, functional and Fourier analysis -- Modulation spaces -- Equivalent definitions of modulation spaces -- Pseudodifferential operators -- Weighted modulation spaces -- Modulation spaces and other function spaces -- Applications to partial differential equations -- A proof of Banach's fixed point theorem -- The Picard-Lindelöf and Peano theorems -- Gronwall's lemma -- Local well-posedness of NLS on Sobolev spaces. 330 $aThis monograph serves as a much-needed, self-contained reference on the topic of modulation spaces. By gathering together state-of-the-art developments and previously unexplored applications, readers will be motivated to make effective use of this topic in future research. Because modulation spaces have historically only received a cursory treatment, this book will fill a gap in time-frequency analysis literature, and offer readers a convenient and timely resource. Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. The focus then expands to the many valuable applications of modulation spaces, such as linear and multilinear pseudodifferential operators, and dispersive partial differential equations. Because it is almost entirely self-contained, these insights will be accessible to a wide audience of interested readers. Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations. 410 0$aApplied and Numerical Harmonic Analysis,$x2296-5009 606 $aFourier analysis 606 $aOperator theory 606 $aPartial differential equations 606 $aFunctional analysis 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aFourier analysis. 615 0$aOperator theory. 615 0$aPartial differential equations. 615 0$aFunctional analysis. 615 14$aFourier Analysis. 615 24$aOperator Theory. 615 24$aPartial Differential Equations. 615 24$aFunctional Analysis. 676 $a515 700 $aBényi$b Árpád$4aut$4http://id.loc.gov/vocabulary/relators/aut$0927211 702 $aOkoudjou$b Kasso A$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484421903321 996 $aModulation Spaces$92083311 997 $aUNINA