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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
Spectrum of operator defined by composition with linear function
This is really a comment, not an answer but I am not empowered. I am taking the liberty of reinterpreting your question (always a dangerous course) since it has already been pointed out that your ope …
4
votes
The derivative of a non-tempered distribution can be tempered?
A distribution is tempered if and only if it is the distributional derivative $D^nF$ of a continuous function $F$ which is $O(x^k)$ for some positive integer. Its primitive is then $D^{n-1}F$ and so …
4
votes
Tightness of Measures, Riesz Representation for locally compact spaces
The proper framework for your question is the so-called strict topology on the space of bounded continuous functions which was introduced for the case of a locally compact space by R.C. Buck in the 50 …
6
votes
Accepted
Fréchet-Kolmogorov compactness Theorem for Lp spaces on manifolds
The result you mention uses the algebraic structure of euclidean space since it involves a form of uniform approxability of the set and its translates. However, there are many criteria for compactne …
1
vote
A sufficient condition for a probability measure to have compact support
The answer in the second case is even easier. In order to avoid circularity, define the Stieltjes transform of a measure only on the complex plane minus the real axis . Then the measure has support …