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Results tagged with fa.functional-analysis
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user 47925
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
Paley-Wiener type theorem for integral functions with compact support
Unni addresses $L^p$ Paley Wiener type theorems for Hankel transforms in (MR0174941). In the introduction, he also lists references for $L^p$ Paley Wiener theorems for Fourier transforms.
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2
votes
1
answer
266
views
Is a Fréchet Montel space distinguished?
Based on a couple of references, it seems that the answer is yes, see for example
Boneta-Dierolf, 1992 and Bierstedt-Bonet, 1989.
However, from a comment to the answer of this MO question, I infer th …
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3
votes
Heuristic interpretation of the 'third index' for Besov and Triebel-Lizorkin spaces
Let us look at the definition of Besov spaces from [Bergh and Löfström, 1976].
Suppose $\varphi:\mathbb{R}\rightarrow\mathbb{R}$ is a Schwartz class function satisfying
the support of $\varphi$ is …
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2
votes
Interpolation between $L_p$ and $B^s_{q,q}$
See Equation (8.33) of Triebel, Spaces of distributions of Besov type on Euclidean n-space. Duality, interpolation, 1973. (MR0348483)
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1
vote
Radial Kernel with Bounded Support and Norm of Gradient Bounded by a Dimension-free Constant
note: This is not a complete answer, but I think it helps clarify the problem.
Since $K$ is radial, the problem can be formulated in terms of the profile function $\phi$. If we let $r=\|x\|_2$, then …
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