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Balanced Colombeau products of the distributions x ± - p and x - p

Blagovest Damyanov (2005)

Czechoslovak Mathematical Journal

Results on singular products of the distributions x ± - p and x - p for natural p are derived, when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusiński in 1966. The results are obtained in the Colombeau algebra of generalized functions, which is the most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.

Boehmians of type S and their Fourier transforms

R. Bhuvaneswari, V. Karunakaran (2010)

Annales UMCS, Mathematica

Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.

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