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 theory of distributions 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. In this classic text the theory is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces; and in this second edition, the notion of the wavefront set of a distribution is introduced. This account will be useful to graduate students and research workers who are inetersted in the applications of analysis in mathematics and mathematical physics.

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