Analytic Partial Differential Equations
François Treves
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Springer International Publishing
Naturwissenschaften, Medizin, Informatik, Technik / Analysis
Beschreibung
This book provides a coherent, self-contained introduction to central topics of Analytic Partial Differential Equations in the natural geometric setting. The main themes are the analysis in phase-space of analytic PDEs and the Fourier–Bros–Iagolnitzer (FBI) transform of distributions and hyperfunctions, with application to existence and regularity questions.
This book provides a unified presentation of a wealth of material that was previously restricted to research articles. In contrast to existing monographs, the approach of the book is analytic rather than algebraic, and tools such as sheaf cohomology, stratification theory of analyticvarieties and symplectic geometry are used sparingly and introduced as required. The first half of the book is mainly pedagogical in intent, accessible to advanced graduate students and postdocs, while the second, more specialized part is intended as a reference for researchers.
Kundenbewertungen
Cauchy-Kovalevskaya Theorem, stratification, regularity of hyperfunction solutions, eikonal equations, phase-functions, analytic partial differential equations, partial differential equations of principal type, Fourier integral operators, differential complexes, Lojaciewicz inequality, hyperfunctions, analytic wave-front set, Ovsyannikov analyticity, microlocal analysis, partial differential equations, FBI transform, Nagano foliations, distribution, pseudodifferential operators