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Informationen zum Autor Christopher D. Sogge is the J. J. Sylvester Professor of Mathematics at The John Hopkins University and the editor-in-chief of the American Journal of Mathematics. His research concerns Fourier analysis and partial differential equations. In 2012, he became one of the Inaugural Fellows of the American Mathematical Society. He is also a fellow of the National Science Foundation, the Alfred P. Sloan Foundation and the Guggenheim Foundation, and he is a recipient of the Presidential Young Investigator Award. In 2007, he received the Diversity Recognition Award from The Johns Hopkins University. Klappentext This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. Zusammenfassung This advanced monograph, concerned with modern treatments of central problems in harmonic analysis, explores the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. New chapters discuss the Duistermaat–Guillemin theorem and results related to the Kakeya conjecture. Inhaltsverzeichnis 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.
