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Results tagged with harmonic-analysis
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user 9652
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.
2
votes
When is a collection of exponentials dense in $L^2(K), |K|<\infty$
Not a full answer, but a question like this stated and answered for $K=]-\infty,\infty[$ in "A class of nonharmonic Fourier series", R. J. Duffin and A. C. Schaeffer, Trans. Amer. Math. Soc. 72 (1952) …
- 12.7k
5
votes
How to do DFT for irregular sampling period ?
If you are looking for software: Have a look at NFFT by Potts, Kreiner and Kunis.
- 12.7k
3
votes
A metric on the set of BV functions, is it mentioned/studied in literature?
This is closely related to the so-called metric of strict convergence which is
$$
d(u,v) = \|u-v\|_{L^1} + |TV(u)-TV(v)|
$$
where $TV(u)$ denoted the total variation of $u$. This is indeed a metric on …
- 12.7k
2
votes
Young’s complement of $ x \mapsto x \, {\log^{+}}(x) $, $ N $-functions and Orlicz spaces
That space should be $L_{\exp}$. Check Bennett and Sharpley's "Interpolation of Operators" Chapter 4.6 or look in Rao and Ren's "Theory of Orlicz Spaces".
- 12.7k
8
votes
Making the Fourier transform quantitative
There are various mathematical formulations of this phenomenon and some of them are quite quantitative.
First, there is the classical Heisenberg uncertainty principle which roughly states that the pr …
- 12.7k
6
votes
Two reference requests: Pinsker's inequality and Pontryagin duality
I found Rudin's "Fourier Analysis on Groups" a good reference for Pontryagin duality. The level of functional analysis there is not too high.
- 12.7k