Screen LibraryLinear partial differential operators in Gevrey spaces /
The book is devoted to new and classical results of the theory of linear partial differential operators in Gevrey spaces. The microlocal approach is adopted, by using pseudo-differential operators, wave front sets and Fourier integral operators.Basic results for Schwartz-distributions, c and analyti...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore ; River Edge, N.J. : |
| Publication Dates: | 1993. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/1550#t=toc |
| Summary: |
The book is devoted to new and classical results of the theory of linear partial differential operators in Gevrey spaces. The microlocal approach is adopted, by using pseudo-differential operators, wave front sets and Fourier integral operators.Basic results for Schwartz-distributions, c and analytic classes are also included, concerning hypoellipticity, solvability and propagation of singularities.Also included is a self-contained exposition of the calculus of the pseudo-differential operators of infinite order. |
| Carrier Form: | 1 online resource (viii,251pages) |
| Bibliography: | Includes bibliographical references (pages 237-249) and index. |
| ISBN: | 9789814360036 (electronic bk.) |
| CLC: | O175.3 |
| Contents: | Introduction -- ch. I. Gevrey functions and ultradistributions. Summary -- 1.1. Notations -- 1.2. Identities and inequalities for factorials and binomial coefficients -- 1.3. Schwartz distributions and [symbol] wave front set -- 1.4. Gevrey functions -- 1.5. Gevrey ultradistributions -- 1.6. Fourier transform in Gevrey spaces -- 1.7. Gevrey wave front sets -- 1.8. Inhomogeneous Gevrey classes -- 1.9. Other generalized Gevrey classes and references -- ch. II. Basic problems and basic operators in Gevrey classes. Summary -- 2.1. The problem of the hypoellipticity -- 2.2. Hypoelliptic operators with constant coefficients -- 2.3. Basic operators of principal type -- 2.4. The problem of the local solvability -- 2.5. Hyperbolic operators with constant coefficients -- 2.6. Other results for operators with constant coefficients -- 2.7. The microlocal point of view -- ch. III. Pseudo-differential operators. Summary -- 3.1. An introduction to the pseudo-differential calculus -- 3.2. Pseudo-differential operators of infinite order -- 3.3. Finite order pseudo-differential operators and applications to the problem of the hypoellipticity -- 3.4. Microlocalization -- 3.5. General operators of principal type -- 3.6. Inhomogeneous pseudo-differential operators -- ch. IV. Operators with multiple characteristics. Summary -- 4.1. Propagation of singularities and hypoellipticity for operators of type [symbol] -- 4.2. Non-solvability for operators of type [symbol] -- 4.3. Operators of type [symbol] -- 4.4. Analytic-hypoelliptic operators which are not hypoelliptic in the [symbol] sense -- 4.5. Additional references. |