00843nam0 2200241 i 450 VAN006486220180724094045.11520080611d1988 |0itac50 baitaIT|||| |||||ˆIl ‰PordenoneCaterina FurlanMilanoElectac1988396 p.ill.29 cm.MilanoVANL000284FurlanCaterinaVANV051655Electa <editore>VANV113606650ITSOL20230915RICABIBLIOTECA DEL DIPARTIMENTO DI LETTERE E BENI CULTURALIIT-CE0103VAN07VAN0064862BIBLIOTECA DEL DIPARTIMENTO DI LETTERE E BENI CULTURALI07CONS Pa Pordenone 768 07 186 20080611 Pordenone743569UNICAMPANIA03855nam 22005895 450 991089017380332120240926130225.03-031-70909-810.1007/978-3-031-70909-8(MiAaPQ)EBC31691830(Au-PeEL)EBL31691830(CKB)36200513800041(MiAaPQ)EBC31691112(Au-PeEL)EBL31691112(DE-He213)978-3-031-70909-8(EXLCZ)993620051380004120240926d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAnalysis and Partial Differential Equations /by Thomas Alazard1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (439 pages)Universitext,2191-66753-031-70908-X Part I Functional Analysis -- 1 Topological Vector Spaces -- 2 Fixed Point Theorems -- 3 Hilbertian Analysis, Duality and Convexity -- Part II Harmonic Analysis -- 4 Fourier Series -- 5 Fourier Transform -- 6 Convolution -- 7 Sobolev Spaces -- 8 Harmonic Functions -- Part III Microlocal Analysis -- 9 Pseudo-Differential Operators -- 10 Symbolic Calculus -- 11 Hyperbolic Equations -- 12 Microlocal Singularities -- Part IV Analysis of Partial Differential Equations -- 13 The Calderón Problem -- 14 De Giorgi’s Theorem -- 15 Schauder’s Theorem -- 16 Dispersive Estimates -- Part V Recap and Solutions to the Exercises -- 17 Recap on General Topology -- 18 Inequalities in Lebesgue Spaces -- 19 Solutions.This textbook provides a modern introduction to advanced concepts and methods of mathematical analysis. The first three parts of the book cover functional analysis, harmonic analysis, and microlocal analysis. Each chapter is designed to provide readers with a solid understanding of fundamental concepts while guiding them through detailed proofs of significant theorems. These include the universal approximation property for artificial neural networks, Brouwer's domain invariance theorem, Nash's implicit function theorem, Calderón's reconstruction formula and wavelets, Wiener's Tauberian theorem, Hörmander's theorem of propagation of singularities, and proofs of many inequalities centered around the works of Hardy, Littlewood, and Sobolev. The final part of the book offers an overview of the analysis of partial differential equations. This vast subject is approached through a selection of major theorems such as the solution to Calderón's problem, De Giorgi's regularity theorem for elliptic equations, and the proof of a Strichartz–Bourgain estimate. Several renowned results are included in the numerous examples. Based on courses given successively at the École Normale Supérieure in France (ENS Paris and ENS Paris-Saclay) and at Tsinghua University, the book is ideally suited for graduate courses in analysis and PDE. The prerequisites in topology and real analysis are conveniently recalled in the appendix.Universitext,2191-6675Differential equationsFunctional analysisFourier analysisDifferential EquationsFunctional AnalysisFourier AnalysisDifferential equations.Functional analysis.Fourier analysis.Differential Equations.Functional Analysis.Fourier Analysis.515.35Alazard Thomas845497MiAaPQMiAaPQMiAaPQBOOK9910890173803321Analysis and Partial Differential Equations4249052UNINA00629nus2 2200217 i 450 CFI030056420251003044138.019960930a19..9999||||0itac50 baitbzu||||||||Paradigma. Filosofia pubblicaNapoliLiguori.Paradigma001UMC09937262001 Paradigma001CFI01624842001 Filosofia pubblicaITIT-00000019960930IT-BN0095 IT-NA0079 IT-NA0070 CFI0300564 01 84 BN BU DPParadigma68389UNISANNIO