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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 …
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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 …
barcelos's user avatar
  • 334
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 …
barcelos's user avatar
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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 …
barcelos's user avatar
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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 …
barcelos's user avatar
  • 334