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Analysis and Partial Differential Equations

Name: Analysis and Partial Differential Equations
Brand: Springer, Berlin
SKU: 46550352
Price: 64.04 EUR
Availability: InStock
Author: Thomas Alazard
ISBN: 9783031709081

Thomas Alazard

Език

Английски език

Книга С меки корици

Код Либристо: 46550352

Издателство Springer, Berlin, ноември 2023

This textbook provides a modern introduction to advanced concepts and methods of mathematical analys... Цялото описание

Код Либристо: 46550352

155 b

64.04 €

125.25 лв

Външен склад Изпращаме след 8-11 дни

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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, 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