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The Analysis of Linear PD Operators. II, Diff. operators With Constant Coefficients

✍ Scribed by Lars Hörmander

Book ID
127420154
Publisher
Springer
Year
2004
Tongue
English
Weight
3 MB
Series
Classics in Mathematics
Edition
2005
Category
Library
ISBN
3540269649

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✦ Synopsis

Vol. I of Lars H?rmander's 4-volume treatise was an exposition of the theory of distributions and Fourier analysis preparing for the study of linear partial differential operators.

The present Vol. II is mainly devoted to operators with constant coefficients. An analysis of the existence and regularity of (fundamental) solutions in the first two chapters is followed by a thorough study of the Cauchy problem. One chapter is devoted to the spectral theory of short range perturbations of operators with constant coefficients, and another presents Fourier-Laplace representations of solutions of homogeneous differential equations with constant coefficients. The last chapter is a study of the closely related subject of convolution operators.

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## Abstract Let __P__(__z__) be a polynomial of degree __n__ with complex coefficients and consider the __n__–th order linear differential operator __P__(__D__). We show that the equation __P__(__D__)__f__ = 0 has the Hyers–Ulam stability, if and only if the equation __P__(__z__) = 0 has no pure im