Questions tagged [generalized-functions]
The generalized-functions tag has no usage guidance.
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Anti-delta function?
Did anyone ever consider a "function" or "distribution" $F(x)$ with the following property:
its integral $\int_a^b F(x)\,dx=0$ for any finite interval $(a,b)$ but $\int_{-\infty}^\...
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Research topics in distribution theory
The theory of distributions is very interesting, and I have noticed that it has many applications especially with regard to PDEs. But what are the research topics in this theory? also in terms of ...
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Wiener measure and Bochner Minlos
I am reading probability theory and I have a question. The Bochner-Minlos theorem roughly says that if we have $E \subset H \subset E^*$ where $H$ is a Hilbert space, then there is a unique measure ...
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English translation of Schwartz's papers on vector-valued distributions
I am interested in systematically studying the theory of vector-valued distributions. The original two papers due to Laurent Schwartz entitled Théorie des distributions à valeurs vectorielles. I & ...
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Are those distributional solutions that are functions, the same as weak solutions?
There are two closely related concepts and I am not sure exactly how close. Consider a partial differential equation. (The coefficients need not be constant but assume they are functions, and not ...