Microlocal Analysis and Spectral Theory
By: edited by Luigi Rodino
Series: NATO ASI Series, Series C: Mathematical and Physical Sciences, 1389-2185 -- 490; NATO ASI series -- 490.
Publisher: Springer Netherlands; Imprint; Springer
Published: 1997
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 452
ISBN-13: 9789401156264
Other titles: Proceedings of the NATO Advanced Study Institute, Il Ciocco, Castelvecchio Pascoli (Lucca), Italy, 23 September-3 October 1996
Description: There has been considerable recent progress in the field of microlocal analysis. In a broad sense the subject is the modern version of the classical Fourier technique for solving partial differential equations, with the localization process taking account of dual variables. The tools of pseudo-differential operators, wave-front sets and Fourier integral operators have now conferred a mature form on the theory of linear partial differential operators in the frame of Schwartz distributions or other generalized functions. At the same time, microlocal analysis has assumed an important role as an independent part of analysis, with other applications throughout mathematics and physics, one major theme being spectral theory for the Schrödinger equation in quantum mechanics. <br/> The papers collected here emphasize the topics of microlocal methods in the study of linear PDEs (analytic-Gevrey regularity of the solutions, elliptic boundary value problems, higher microlocalization), and applications to spectral theory (Schrödinger equation, asymptotic behavior of the eigenvalues, semi-classical analysis in large dimensions and statistical mechanics). <br/> <em>Audience:</em> Accessible to a wide audience, including graduate students in analysis and non-specialists from mathematics and physics.