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Introduction to the theory of distributions

By: Contributor(s): Material type: TextTextLanguage: English Publication details: Cambridge Cambridge University Press 1998Edition: 2Description: ix, 175pISBN:
  • 0521649714 (PB)
Subject(s):
Contents:
1. Test functions and distributions 2. Differentiation, and multiplication by smooth functions 3. Distributions with compact support 4. Tensor products 5. Convolution 6. Distribution kernels 7. Coordinate transformations and pullbacks 8. Tempered distributions and Fourier transforms 9. Plancherel's theorem, and Sobolev spaces 10. The Fourier-Laplace transform 11. The calculus of wavefront sets
Summary: The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book adopts this course and is based on graduate lectures given over a number of years." "This account should be useful to graduate students and research workers who are interested in the applications of analysis in mathematics and mathematical physics.
Item type: BOOKS
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IMSc Library 517.98 FRI (Browse shelf(Opens below)) Available 38761

Includes index

Includes bibliography (p. 170) and references

1. Test functions and distributions 2. Differentiation, and multiplication by smooth functions 3. Distributions with compact support 4. Tensor products 5. Convolution 6. Distribution kernels 7. Coordinate transformations and pullbacks 8. Tempered distributions and Fourier transforms 9. Plancherel's theorem, and Sobolev spaces 10. The Fourier-Laplace transform 11. The calculus of wavefront sets

The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book adopts this course and is based on graduate lectures given over a number of years." "This account should be useful to graduate students and research workers who are interested in the applications of analysis in mathematics and mathematical physics.

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The Institute of Mathematical Sciences, Chennai, India