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Title: Three-Dimensional Operational Calculi for Nonlocal Evolution Boundary Value Problems
Other Titles: Тримерни операционни смятания за нелокални еволюционни гранични задачи
Authors: Dimovski, Ivan
Tsankov, Yulian
Keywords: Duhamel Convolution
Convolution Algebra
Multiplier Fraction
Divisor of Zero
Numerical Operator
Issue Date: 2011
Publisher: Union of Bulgarian Mathematicians
Citation: Union of Bulgarian Mathematicians, Vol. 40, No 1, (2011), 169p-175p
Abstract: Direct algebraic operational calculi for functions u(x, y, t), continuous in a domain of the form D = [0, a] × [0, b] × [0, ∞), are proposed. Along with the classical Duhamel convolution, the construction uses also two non-classical convolutions for the operators ∂2x and ∂2y. These three one-dimensional convolutions are combined into one three-dimensional convolution u ∗ v in C(D). Instead of J. Mikusi´nski’s approach, based on convolution fractions, we develop systematically an alternative approach, based on the multiplier fractions of the convolution algebra (C(D), ∗). *2000 Mathematics Subject Classification: 44A35, 44A45, 35K20, 35K15, 35J25.
Description: Иван Христов Димовски, Юлиан Цанков Цанков - Построени са директни операционни смятания за функции u(x, y, t), непрекъснати в област от вида D = [0, a] × [0, b] × [0, ∞). Наред с класическата дюамелова конволюция, построението използва и две некласически конволюции за операторите ∂2x и ∂2y. Тези три едномерни конволюции се комбинират в една тримерна конволюция u ∗ v в C(D). Вместо подхода на Я. Микусински, основаващ се на конволюционни частни, се развива алтернативен подход с използване на мултипликаторните частни на конволюционната алгебра (C(D), ∗).
ISBN: 1313-3330
Appears in Collections:Mathematics and Education in Mathematics, 2011

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