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Results tagged with fa.functional-analysis
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user 132216
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
0
answers
118
views
Is it possible to define a Bochner integral for a $S'(\mathbb R^d)$-valued function?
I apologize in advance for the rather vague question.
While reading the book White noise distribution theory by H.H. Kuo, in particular the section 13.3 I came across the following statement (I'll par …
- 515
5
votes
2
answers
281
views
Existence of a solution for this hypoelliptic-alike PDE
I know that this question may result rater vague and somehow out of context, still I am hoping you could help me.
Assume we have the following equation
\begin{align}
\boxed{\partial_t u(t,x,z)=\mathca …
- 6,367
1
vote
0
answers
295
views
Gaussian measures on infinite dimensional spaces
On Zabczyk & Da Prato book about infinite dimensional SDEs they introduce the idea of Gaussian measures in infinite dimensional Banach spaces. They do so by means of Fernique theorem.
In the White No …
3
votes
0
answers
87
views
Doubt when calculating the S-transform of Hida differential operator
Assume we have a Hida test function $\varphi\in (\mathcal S)$, and $y\in \mathcal S'(\mathbb R)$. Define the Gateaux directional derivative of $\varphi$ (in the direction of $y$) by:
$$D_y\varphi(x):= …
- 515
3
votes
1
answer
246
views
Question regarding the Wick tensor in white noise analysis
I have a question regarding the definition of Wick tensor in the framework of the white noise analysis.
To put some context to the question we start with the following Gel'fand triple
$$S(\mathbb R)\ …
- 10.3k