Fourier Integrals in Classical Analysis

ISBN-13: 9781107120075 / Angielski / Twarda / 2017 / 348 str.

Christopher D. Sogge

Opis

This advanced monograph is concerned with modern treatments of central problems in harmonic analysis.

Recenzje

'Fourier Integrals and Classical Analysis is an excellent book on a beautiful subject seeing a lot of high-level activity. Sogge notes that the book evolved out of his 1991 UCLA lecture notes, and this indicates the level of preparation expected from the reader: that of a serious advanced graduate student in analysis, or even a beginning licensed analyst, looking to do work in this area. But a lot of advantage can be gained even by fellow travelers, all modulo enough mathematical maturity, training, and Sitzfleisch.' Michael Berg, MAA Reviews

Spis treści

Background; 1. Stationary phase; 2. Non-homogeneous oscillatory integral operators; 3. Pseudo-differential operators; 4. The half-wave operator and functions of pseudo-differential operators; 5. Lp estimates of Eigenfunctions; 6. Fourier integral operators; 7. Propagation of singularities and refined estimates; 8. Local smoothing of fourier integral operators; 9. Kakeya type maximal operators; Appendix. Lagrangian subspaces of T*Rn; References; Index of Notation; Index.