This text is based on lectures given by the author at the advanced undergaraduate and graduate levels in Measure theory, Functional Analysis, Bannach Algebras, Spectral Theory (of bounded and unbounded operators), Semigroups of Operators, Probability and Mathematical Statistics, and Partial Differential Equations. The first 10 chapters discuss theoretical methods in Measure Theory and Functional Analysis and contain over 120 end of chapter exercises. the final two chapters apply theory to applications in Probability Theory and Partial Differential Equations.
Author(s): Shmuel Kantorovitz
Series: Oxford Graduate Texts in Mathematics, 8
Publisher: Oxford University Press, USA
Year: 2003
Language: English
Pages: 448
Introduction to Modern Analysis......Page 1
oxford graduate texts in mathematics......Page 3
Preface......Page 7
Contents......Page 9
1 Measures......Page 13
2 Construction of measures......Page 69
3 Measure and topology......Page 89
4 Continuous linearfunctionals......Page 114
5 Duality......Page 135
6 Bounded operators......Page 165
7 Banach algebras......Page 182
8 Hilbert spaces......Page 215
9 Integral representation......Page 235
10 Unbounded operators......Page 270
Application I Probability......Page 295
Application II Distributions......Page 376
Bibliography......Page 433
Index......Page 437
chapter01.pdf......Page 447
chapter02.pdf......Page 469
chapter03.pdf......Page 484
chapter04.pdf......Page 504
chapter05.pdf......Page 517
chapter06.pdf......Page 527
chapter07.pdf......Page 549
chapter08.pdf......Page 575
chapter09.pdf......Page 605
chapter10.pdf......Page 623
