Questions tagged [generalized-functions]

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30 questions
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Covergence of fractional Taylor series

Let $f(x)$ be a function that is continuous and infinitely smooth on entire $\mathbb R$. Let's consider Taylor-Maclaurin series for this function: $$f(x) = \sum_{0}^{∞}\frac{f^n(x_0)(x-x_0)^n}{n!}$$ ...
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Make mathematical sense of the Dirac well Potential Equation

A classical problem in quantum mechanics involving the Dirac Delta function is given by $$y''+(\delta(x)-\lambda^2)y=0.$$ Then, to find ''bound states'', you solve on the right and find the ...
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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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How to define a generalized differential form through its values on submanifolds

Suppose we're in $\mathbb R^n$, and we have a function on line segments ,$\omega(I)$, with values in $\mathbb R$. Give sufficient conditions for $\omega$ to be given by a generalized 1-form (that is, ...
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Sequential continuity of linear operators

Let $u\colon L\to M$ be a linear map of locally convex linear topological vector spaces. Assume that $u$ is sequentually continuous, i.e. maps convergent sequences to convergent ones. (This notion is ...