Analysis and partial differential equations:
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 concep...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham
Springer
[2024]
|
| Ausgabe: | 2024 |
| Schriftenreihe: | Universitext
|
| Schlagwörter: | |
| Zusammenfassung: | 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 |
| Umfang: | xiv, 439 Seiten 235 mm |
| ISBN: | 9783031709081 |
| ISSN: | 0172-5939 |
Internformat
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| 520 | |a 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 | ||
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035260440 | |
Datensatz im Suchindex
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| discipline | Mathematik |
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| format | Book |
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| id | DE-604.BV049921877 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-28T19:09:24Z |
| institution | BVB |
| isbn | 9783031709081 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035260440 |
| oclc_num | 1477599845 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | xiv, 439 Seiten 235 mm |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Alazard, Thomas Verfasser (DE-588)1084007835 aut Analysis and partial differential equations Thomas Alazard Cham Springer [2024] xiv, 439 Seiten 235 mm txt rdacontent n rdamedia nc rdacarrier Universitext 0172-5939 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 bicssc bisacsh Functional analysis Fourier analysis Differential equations Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Alazard, Thomas Analyse et équations aux dérivées partielles 2023 Erscheint auch als Online-Ausgabe 978-3-031-70909-8 |
| spellingShingle | Alazard, Thomas Analysis and partial differential equations bicssc bisacsh Functional analysis Fourier analysis Differential equations Partielle Differentialgleichung (DE-588)4044779-0 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4018916-8 |
| title | Analysis and partial differential equations |
| title_alt | Analyse et équations aux dérivées partielles |
| title_auth | Analysis and partial differential equations |
| title_exact_search | Analysis and partial differential equations |
| title_full | Analysis and partial differential equations Thomas Alazard |
| title_fullStr | Analysis and partial differential equations Thomas Alazard |
| title_full_unstemmed | Analysis and partial differential equations Thomas Alazard |
| title_short | Analysis and partial differential equations |
| title_sort | analysis and partial differential equations |
| topic | bicssc bisacsh Functional analysis Fourier analysis Differential equations Partielle Differentialgleichung (DE-588)4044779-0 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | bicssc bisacsh Functional analysis Fourier analysis Differential equations Partielle Differentialgleichung Funktionalanalysis |
| work_keys_str_mv | AT alazardthomas analysisandpartialdifferentialequations |