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Results tagged with cv.complex-variables
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user 359
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
2
votes
Why do functions in complex analysis behave so well? (as opposed to functions in real analysis)
A complex function is analytic if and only if locally it can be represented by a power series. This means that (at least locally) an analytic function is determined by countable data (namely, the Tay …
- 1,412
17
votes
2
answers
2k
views
Getting a differential equation for a function from a functional equation of its Mellin tran...
If $f$ is a locally integrable function then its Mellin transform
$\mathcal{M}[f]$ is defined by
$$ \mathcal{M}[f] (s) = \int_0^{\infty} x^{s - 1} f (x) dx . $$
This integral usually converges in a st …
- 1,412
4
votes
Getting a differential equation for a function from a functional equation of its Mellin tran...
By defining the Mellin transform for distributions as for instance done in Transform Analysis of Generalized Functions by O. Misra, J. Lavoine it follows that the functional equation for $F(s)$ transl …
- 1,412