報告題目: ON MULTIPLICATION OF DISTRIBUTIONS
報告摘要: The distributions (or generalized functions) were introduced by S.L. Sobolev and L.Schwartz and now the distribution theory is an attractive instrument in analysis of numerous problems in mathematical physics and dierential equations theory. As is known it is impossible to dene the product of arbitrary generalized functions in the classical theory of distributions. This is a crucial obstacle for applying distributions' theory to equations with generalized coecients and non-linear problems. The common approach to solve the problem of multiplication of distributions from a given space of E consists in constructing a dierential algebra G(E), such that its elements preserve general properties of distributions. Such algebras G are called Colombeau type algebras and their elements are called new generalized functions or mnemofunctions. In the talk we present a certain example of the algebra of mnemofunctions and undertake the calculation of products of a number of distributions within the frames of this theory.
Anatolij Antonevich教授, Professor in Faculty of Mathematics and Mechanics BSU.