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Harmonic generalized functions in generalized function algebras
Monatshefte für Mathematik, 2009We investigate basic properties of harmonic generalized functions within the framework of J. F. Colombeau’s theory of generalized functions. In particular, we present various theorems concerning the Maximum principle, Liouville’s theorem, singularities and Poisson formula.
Pilipović, Stevan +1 more
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Journal of Applied Probability, 1982
There are described in the literature many spaces of what are variously described as generalized functions, distributions, or improper functions. This article introduces another. The new space is like that of M. J. Lighthill in containing the Fourier transform of every element and in having a particularly simple theory of trigonometric and Fourier ...
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There are described in the literature many spaces of what are variously described as generalized functions, distributions, or improper functions. This article introduces another. The new space is like that of M. J. Lighthill in containing the Fourier transform of every element and in having a particularly simple theory of trigonometric and Fourier ...
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Generating Functions for Hermite Functions
Canadian Journal of Mathematics, 1959Hermite's function Hn(x) is denned for all complex values of x and n bywhere F (α; γ; x) is Kummer's function with the customary indices omitted. It satisfies the differential equation1.1of whichis a second solution. Every solution of (1.1) is an entire function.
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Generating functions of the hypergeometric functions
Journal of Mathematical Physics, 1974The Lie algebra, which was introduced in a previous paper to treat the hypergeometric functions by Lie theory techniques, is used to derive generating functions of the hypergeometric functions. Several generating functions are obtained from the theory of multiplier representations. Weisner's method is also applied, giving another generating function.
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Generating Functions for Ultraspherical Functions
Canadian Journal of Mathematics, 1968The ultraspherical function1.1for |1 — x| < 2 is a solution of the differential equation1.2This equation has two independent solutions; of the two, only Pn(λ)(x) is analytic at x = 1, aside for some special values of λ, which we shall not consider.
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Generating Functions and Characteristic Functions
1992These functions are of considerable use in theoretical probability, i.e., proving probability theorems. They are also of use to us when we wish to put two distributions together. Consider x = x 1 + x 2 + ... + x n, where x 1 is distributed according to one distribution, x 2 according to another, etc.
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Composition and functions of bacterial membrane vesicles
Nature Reviews Microbiology, 2023Masanori Toyofuku +2 more
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