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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

2 votes
1 answer
1k views

Weierstrass factorization theorem in several variables

Can one indicate to me the Weierstrass factorization theorem in several variables (real or complex). In one complex variable the result is well known. Thank you in advance.
Safwane's user avatar
  • 1,197
0 votes
2 answers
399 views

functional equation

I have the following question: Let $f$ be an analytic function satisfying the functional equation: $f(z)=u(z)f(a-z)$ where $a$ is a real constant. Let $g$ be another function satisfying the same funct …
Safwane's user avatar
  • 1,197
-4 votes
1 answer
200 views

How I can choose $(t_1,t_2,...,t_{r}) \in (0,1)^{r}$ such that $f^{(k)}\left(1-2\prod_{j=1}^...

Let $f:\mathbb{R} \to \mathbb{R}$ be a real analytic function. Assume that $f$ has simple trivial zeros at each nonpositive integer. Then, all the $k$-th derivatives $f^{(k)}$ of $f$ have necessarily …
Safwane's user avatar
  • 1,197