Items related to Distributions and Pseudo-Differential Operators
Synopsis
The theory of distributions is an extension of classical analysis which has acquired a particular importance in the modern mathematics and mathematical physics. This text presents some of its topics (eg fundamental definitions and properties, differentiation and mutiplication by smooth functions, temperate distributions and their Fourier transform, the Hs(IR") and the B1,s (IR") spaces, distributions with compact support). The rest of the monograph deals with some classes of pseudo-differential operators in the framework of the theory of distributions and of the operator theory. The presentation used here is "elementary" and with full details, using only knowledge in advanced calculus in several variables and in elementary functional analysis. It should be of interest and useful to graduate students and research workers who are interested in functional analysis and in operator theory. Part of the material here enclosed (relating to pseudo-differential operator theory) appears for the first time in monograph form. The present text is based on graduate lectures given in Canada (at the Canadian Mathematical Congress, 1965 and at the Universite-de Montreal over a number of years).
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