The Analysis of Linear Partial Differential Operators I : Distribution Theory and Fourier Analysis
Material type: TextLanguage: English Series: Classics in mathematicsPublication details: Heidelberg Springer 2003Edition: 2nd edDescription: XI, 440pISBN: 9783540006626 (PB)Subject(s): Analysis | Applied Mathematics | MathematicsCurrent library | Home library | Call number | Materials specified | Status | Notes | Date due | Barcode |
---|---|---|---|---|---|---|---|
IMSc Library | IMSc Library | 517.956 HOR (Browse shelf (Opens below)) | Not for loan | New Arrivals Displayed Till 30th November 2024 | 78242 |
Includes Bibilography (420-436) and Indexes
I. Test Functions Summary
II. Definition and Basic Properties of Distributions
III. Differentiation and Multiplication by Functions
IV. Convolution
V. Distributions in Product Spaces
VI. Composition with Smooth Maps
VII. The Fourier Transformation Laplace Transforms
VIII. Spectral Analysis of Singularities
IX. Hyperfunctions
The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differential equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of general interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration
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