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Results tagged with harmonic-analysis
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user 47925
Harmonic analysis is a generalisation of Fourier analysis that studies the properties of functions. Check out this tag for abstract harmonic analysis (on abelian locally compact groups), or Euclidean harmonic analysis (eg, Littlewood-Paley theory, singular integrals). It also covers harmonic analysis on tube domains, as well as the study of eigenvalues and eigenvectors of the Laplacian on domains, manifolds and graphs.
4
votes
2
answers
304
views
interpretation of a singular integral
There is a post on MSE about a principal value integral in this paper. It has not received much attention even with a bounty, and since it concerns a published paper, I believe this is a better forum …
- 323
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 …
- 323
2
votes
How to get Fourier–Stieltjes transform on $\mathbb R$ from the nice function on $\mathbb T$ ...
I suspect that you meant
\begin{equation*}
\widehat{f}(n)
=
\frac{1}{2\pi}
\int_{-\pi}^{\pi}
f(e^{i\theta})
e^{-in\theta}
d\theta
\end{equation*}
in which case
\begin{equation*}
F(x)
=
f(e^{ix})
=
\ …
- 323
1
vote
0
answers
148
views
Convolution in Hardy spaces
Question Are there non-trivial restrictions on the coefficients of functions in Hardy spaces ($H_p(\mathbb{D})$, $p<1$) that make a subspace that is closed under convolution?
Definition The Hardy spa …
- 323