Distribution theory 06-TED410
The theory of distributions was developed in the middle of the 20th century mainly by French mathematician L. Schwartz. The main reason for the emergence of this theory was the need to extend differentiation which appeared in the field of mathematical physics. Generally, one can say that distributions are objects which result from the differentiation of continuous functions. Within its 50 years of existence the theory of distribution became an important branch of mathematics and an essential tool in the theory of partial differential equations. It also has various links to other mathematical branches such as harmonic analysis, for example. The purpose of the course is to present the basic notions and theorems of the theory and some examples of its applications.
Bibliography
R. Strichartz, A Guide to Distribution Theory. J. Musielak, Wstęp do analizy funkcjonalnej, rozdział o dystrybucjach. L. Hörmander, The Analysis of Linear Partial Differential Operators, tom I. W. Rudin, Functional Analysis, rozdział poświęcony teorii dystrybucji (dostępne jest także tłumaczenie rosyjskie).;
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