Displaying similar documents to “Improper integrals of distributions”

Distributions that are functions

Ricardo Estrada (2010)

Banach Center Publications

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It is well-known that any locally Lebesgue integrable function generates a unique distribution, a so-called regular distribution. It is also well-known that many non-integrable functions can be regularized to give distributions, but in general not in a unique fashion. What is not so well-known is that to many distributions one can associate an ordinary function, the function that assigns the distributional point value of the distribution at each point where the value exists, and that...

The elementary theory of distributions (II)

Jan Mikusiński, Roman Sikorski

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CONTENTS Introduction................................................................................... 3 § 1. Terminology and notation.................................................................................... 4 § 2. Uniform and almost uniform convergence....................................................... 6 § 3. Fundamental sequences of smooth functions............................................... 6 § 4. The definition of distributions................................................................................

On the support of Fourier transform of weighted distributions

Martha Guzmán-Partida (2010)

Commentationes Mathematicae Universitatis Carolinae

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We give sufficient conditions for the support of the Fourier transform of a certain class of weighted integrable distributions to lie in the region x 1 ≥ 0 and x 2 ≥ 0 .