Analysis and Partial Differential Equations
Thomas Alazard
Broschiertes Buch

Analysis and Partial Differential Equations

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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...