Displaying similar documents to “A new theory of Operational Calculus”

The elementary theory of distributions (I)

J. Mikusiński, R. Sikorski

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CONTENTSIntroduction........................................................................................................... 3§ 1. The abstraction principle............................................................................... 4§ 2. Fundamental sequences of continuous functions......................................... 5§ 3. The definition of distributions........................................................................ 9§ 4. Distributions as a generalization of the...

The elementary theory of distributions (II)

J. Mikusiński, R. Sikorski

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CONTENTSIntroduction................................................................................... 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................................................................................

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...