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Results tagged with fa.functional-analysis
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user 6153
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
Elliptic function with constant real part on the unit square diagonals?
Well, again you seem to have a constant multiple of the Weierstrass P-function, plus a constant. There is a formula in this case for P((1 + i)z), not just for P(2z) as there is for any period lattice …
- 12.6k
3
votes
Special values of a doubly periodic meromorphic function
As a meromorphic doubly-periodic function, it is an elliptic function in the classical sense. You didn't mention the fact that it is an even function, but that also helps. The poles are double, so tha …
- 12.6k
11
votes
Grothendieck on topological vector spaces
It seems clear enough to me that Grothendieck was (perhaps is) sui generis as a mathematician, something that can be said of a few other mathematicians in each of the 19th and 20th centuries (e.g. Ram …
- 12.6k
2
votes
Reference for complex analysis jargon
Conformal radius of a domain and Transfinite diameter seem to have most of these terms; see also http://en.wikipedia.org/wiki/Conformal_radius .
- 17.1k
3
votes
Characterization of closed subspaces of $ L^2(R)$
I wouldn't say there is "nothing special" about $ L^2(R)$, which is a Hilbert space. Abstractly the structure of its closed subspaces (as orthocomplemented lattice, say) is the same as for any other s …
- 12.6k
17
votes
Is there a "crash-course" book on Abelian varieties (e.g., an introduction for physicists)?
Topics in Complex Function Theory, Abelian Functions and Modular Functions of Several Variables by C. L. Siegel is a standard reference using complex function theory. There are older works (e.g. H. F. …
- 12.6k
9
votes
Is square of Delta function defined somewhere?
There are whole theories in microlocal analysis that deal with the issues here, I believe. Some heuristics are that the "singular support" of a distribution controls what it can be multiplied by in a …
- 12.6k
9
votes
Why is the Hahn-Banach theorem so important?
Interestingly, from this angle, Jean Dieudonné in his huge treatise on analysis gets away without it (IIRC). He makes part of it into an exercise? The reason being, apparently, that he approaches anal …
- 12.6k