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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Analytic Partial Differential Equations
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Analytic Partial Differential Equations
François Treves (Gebundene Ausgabe, Englisch)
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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. The book begins by establishing the… fundamental properties of analytic partial differential equations, starting with the Cauchy–Kovalevskaya theorem, before presenting an integrated overview of the approach to hyperfunctions via analytic functionals, first in Euclidean space and, once the geometric background has been laid out, on analytic manifolds. Further topics include the proof of the Lojaciewicz inequality and the division of distributions by analytic functions, a detailed description of the Frobenius and Nagano foliations, and the Hamilton–Jacobi solutions of involutive systems of eikonalequations. The reader then enters the realm of microlocal analysis, through pseudodifferential calculus, introduced at a basic level, followed by Fourier integral operators, including those with complex phase-functions ( à la Sjöstrand). This culminates in an in-depth discussion of the existence and regularity of (distribution or hyperfunction) solutions of analytic differential (and later, pseudodifferential) equations of principal type, exemplifying the usefulness of all the concepts and tools previously introduced. The final three chapters touch on the possible extension of the results to systems of over- (or under-) determined systems of these equations—a cornucopia of open problems. 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
27.04.2022
Sprache
Englisch
EAN
9783030940546
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Grundlehren der mathematischen Wissenschaften
Sonderedition
Nein
Autor
François Treves
Seitenanzahl
1228
Einbandart
Gebundene Ausgabe
Autorenporträt
François Treves has worked in the field of partial differential equations for 65 years, publishing 17 books and over 150 papers. His well-known contributions to the field include his work with Louis Nirenberg on the local solvability of linear PDEs, his contributions to the theory of locally integrable structures (presented in his book
Schlagwörter
partial differential equations, analytic partial differential equations, distribution, microlocal analysis, hyperfunctions, Ovsyannikov analyticity, FBI transform, analytic wave-front set, pseudodifferential operators, Fourier integral operators, partial differential equations of principal type, differential complexes, phase-functions, Cauchy-Kovalevskaya Theorem, Lojaciewicz inequality, stratification, Nagano foliations, eikonal equations, regularity of hyperfunction solutions
Thema-Inhalt
PBK - Mathematische Analysis, allgemein
PBKJ - Differentialrechnung und -gleichungen
PBKF - Funktionalanalysis und Abwandlungen
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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