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Results tagged with fa.functional-analysis
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user 24309
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
3
votes
Accepted
How I can choose $(t_1,t_2,...,t_{r}) \in (0,1)^{r}$ such that $f^{(k)}\left(1-2\prod_{j=1}^...
As your question is stated, nothing guarantees that $f^{(k)}$ has a single simple zero. The fact that you introduce extra paremeters cannot change that fact! So, in general, the answer is: there is no …
- 5,428
9
votes
Accepted
Investigation of $\sum \limits_{k=-\infty}^\infty \frac{x^{k+n}}{ \Gamma(k+n+1)}$ where $n \...
Set $a:=1+n\in \mathbb C$ and assume $a\notin\mathbb Z$; we use the variable $z:=1/x$. The question has already been answered in the comments: the power series $$S(z):=\sum_{k=0}^\infty \frac{z^k}{\Ga …
- 5,428
5
votes
Abstract ODE; PDE; uniqueness of solution
It is true if $A$ is assumed bounded (as can be found in Section 2 of the reference given by Andras Batkai). An "elementary proof" consists in proving the fundamental theorem of calculus, that is for …
- 5,428
8
votes
5
answers
521
views
Reference for : a Fréchet nuclear space is Montel
I'm looking for a reference to cite regarding the property presented in the title: "Closed and bounded sets of a nuclear Fréchet space are compact"
Thank you in advance for the help!
- 5,428
9
votes
Can the topological algebra of analytic functions be endowed with a norm that defines the na...
There is an elementary answer. Let $D$ be any domain of $\mathbb{C}$. The usual derivation operator $\partial : \mathcal{O}(D)\to \mathcal{O}(D)$ is continuous for the topology of uniform convergence …
- 5,428
2
votes
Accepted
Composite families of formal power series over $\mathbb C$ as algebraic variety
For those interested in the question, see my paper on the subject http://fr.arxiv.org/abs/1308.6371v2 , section 6.
- 5,428
3
votes
1
answer
279
views
Composite families of formal power series over $\mathbb C$ as algebraic variety
I was led to prove that the set of composite families $(f_j)_{j \leq k}$ of germs at $0\in \mathbb C^m$ of a holomorphic function (composite = sharing a common divisor belonging to the maximal ideal) …
- 5,428