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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.
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
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