Classical Microlocal Analysis in the Space of Hyperfunctions
Seiten
2000
Springer Berlin (Verlag)
978-3-540-67603-4 (ISBN)
Springer Berlin (Verlag)
978-3-540-67603-4 (ISBN)
This book develops "Classical Microlocal Analysis" in the spaces of hyperfunctions and microfunctions, which makes it possible to apply the methods in the distribution category to the studies on partial differential equations in the hyperfunction category. Here "Classical Microlocal Analysis" means that it does not use "Algebraic Analysis." The main tool in the text is, in some sense, integration by parts. The studies on microlocal uniqueness, analytic hypoellipticity and local solvability are reduced to the problems to derive energy estimates (or a priori estimates). The author assumes basic understanding of theory of pseudodifferential operators in the distribution category.
The book develops "Classical Microlocal Analysis" in the spaces of hyperfunctions and microfunctions, which makes it possible to apply the methods in the distribution category to the studies on partial differential equations in the hyperfunction category. Here "Classical Microlocal Analysis" means that it does not use "Algebraic Analysis." The main tool in the text is, in some sense, integration by parts. The studies on microlocal uniqueness, analytic hypoellipticity and local solvability are reduced to the problems to derive energy estimates (or a priori estimates). The author assumes basic understanding of theory of pseudodifferential operators in the distribution category.
The book develops "Classical Microlocal Analysis" in the spaces of hyperfunctions and microfunctions, which makes it possible to apply the methods in the distribution category to the studies on partial differential equations in the hyperfunction category. Here "Classical Microlocal Analysis" means that it does not use "Algebraic Analysis." The main tool in the text is, in some sense, integration by parts. The studies on microlocal uniqueness, analytic hypoellipticity and local solvability are reduced to the problems to derive energy estimates (or a priori estimates). The author assumes basic understanding of theory of pseudodifferential operators in the distribution category.
Hyperfunctions.- Basic calculus of fourier integral operators and pseudodifferential operators.- Analytic wave front sets and microfunctions.- Microlocal uniqueness.- Local solvability.
"This book will be very useful to everyone who wishes to work in the area of analytic coefficient partial differential equations by using methods from the usual distribution theory." (Alberto Parmeggiani, zbMATH 0949.35003, 2022)
“This book will be very useful to everyone who wishes to work in the area of analytic coefficient partial differential equations by using methods from the usual distribution theory.” (Alberto Parmeggiani, zbMATH 0949.35003, 2022)
| Erscheint lt. Verlag | 23.6.2000 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | X, 370 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 498 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | analytic hypoellipticity • Calculus • differential equation • hyperfunction • local solvability • microlocal analysis • microlocal uniqueness • MSC-Classification: 35-02 • partial differential equation • Partial differential equations • Partielle Differenzialgleichungen |
| ISBN-10 | 3-540-67603-1 / 3540676031 |
| ISBN-13 | 978-3-540-67603-4 / 9783540676034 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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