國立高雄大學圖資館 |

登入

回首頁

Analysis and partial differential equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Analysis and partial differential equationsby Thomas Alazard.
作者:	Alazard, Thomas.
出版者:	Cham :Springer Nature Switzerland :2024.
面頁冊數:	xiv, 439 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Differential equations, Partial.
電子資源:	https://doi.org/10.1007/978-3-031-70909-8
ISBN:	9783031709098$q(electronic bk.)

Analysis and partial differential equations
Alazard, Thomas.

Analysis and partial differential equations[electronic resource] /by Thomas Alazard. - Cham :Springer Nature Switzerland :2024. - xiv, 439 p. :ill., digital ;24 cm. - Universitext,2191-6675. - Universitext..

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.

ISBN: 9783031709098$q(electronic bk.)

Standard No.: 10.1007/978-3-031-70909-8doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.35

Analysis and partial differential equations
LDR:03226nmm a2200349 a 4500 001 669599
003 DE-He213
005 20240926130225.0
006 m d
007 cr nn 008maaau
008 250120s2024 sz s 0 eng d
020 $a 9783031709098$q(electronic bk.)
020 $a 9783031709081$q(paper)
024 7 $a 10.1007/978-3-031-70909-8 $2 doi
035 $a 978-3-031-70909-8
040 $a GP $c GP
041 1 $a eng $h fre
050 4 $a QA377
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.35 $2 23
090 $a QA377 $b .A324 2024
100 1 $a Alazard, Thomas. $3 880712
240 1 0 $a Analyse et équations aux dérivées partielles. $l English
245 1 0 $a Analysis and partial differential equations $h [electronic resource] / $c by Thomas Alazard.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a xiv, 439 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 2191-6675
505 0 $a 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.
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.
650 0 $a Differential equations, Partial. $3 189753
650 0 $a Mathematical analysis. $3 186133
650 1 4 $a Differential Equations. $3 285983
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Fourier Analysis. $3 273776
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Universitext. $3 558272
856 4 0 $u https://doi.org/10.1007/978-3-031-70909-8
950 $a Mathematics and Statistics (SpringerNature-11649)