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Zbl 0712.35001
Hörmander, Lars
The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis. 2nd ed. (English)
[B] Grundlehren der Mathematischen Wissenschaften, 256. Berlin etc.: Springer-Verlag. xi, 440 p. DM 69.00/pbk; DM 128.00/hbk (1990). ISBN 3-540-52343-X/pbk; ISBN 3-540-52345-6/hbk

For a review of the first edition, see Zbl 0521.35001. \par 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 a beginning of a specialized course in partial differential equations. In particular it could serve as an introduction to harmonic analysis. 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. Also rather complete but brief solutions are given. As in the revised printing of Volume II (see Zbl 0687.35002) a number of minor flows have been corrected. Also the bibliography has been updated and slightly enlarged.
MSC 2000:
*35-02 Research monographs (partial differential equations)
42-02 Research monographs (Fourier analysis)
46-02 Research monographs (functional analysis)
35A22 Transform methods (PDE)
35B40 Asymptotic behavior of solutions of PDE
35A05 General existence and uniqueness theorems (PDE)
35L99 Hyperbolic equations and systems
42Bxx Fourier analysis in several variables
46Fxx Generalized functions, etc.
43-02 Research monographs (abstract harmonic analysis)

Keywords: distribution theory; harmonic analysis; regularization; quasi- analyticity; localization; Whitney extension theorem; convolution; subharmonic distributions; plurisubharmonic functions; singularity; wave front set; micro hyperbolicity

Citations: Zbl 0521.35001; Zbl 0687.35002

Cited in: Zbl 1242.22015 Zbl 1222.81276 Zbl 1087.46027 Zbl 1072.35180 Zbl 1028.35001 Zbl 0893.35144 Zbl 0868.35047

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Highlights
Scientific prize winners of the ICM 2010
Overhang
Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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