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Results tagged with harmonic-analysis
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user 5371
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.
20
votes
Accepted
Borel set plus a closed set = Borel
No. Erdös and Stone showed that the sum of two subsets $E$, $F\subset\mathbb R$ may not be Borel even if one of them is compact and the other is $G_\delta$ (see "On the Sum of Two Borel Sets", Proc. A …
- 22.3k
8
votes
Reference for complex analysis jargon
I would say these concepts rather belong to the field of potential theory. You will find most of the definitions and a fairly advanced treatment of the subject in Logarithmic Potentials with External …
- 22.3k
20
votes
Intuition for the Hardy space $H^1$ on $R^n$
In many ways $H^1$ is just a natural substitute for $L^1$.
A typical $H^1$ function is a $1$-atom, i.e. a function $\phi\in L^1(\mathbb R^n)$ such that the support of $\phi$ is contained in some bal …
- 22.3k