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Results tagged with harmonic-analysis
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user 36735
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
Square-integrability of non-holomorphic Poincare series
Computation of the Fourier expansion of non-holomorphic Poincare series is due to Selberg, in his survey paper "On the estimation of Fourier coefficients of modular forms. 1965 Proc. Sympos. Pure Math …
- 1,692
5
votes
0
answers
210
views
Explicit description of the Plancherel measure for $GL_n(\mathbb{R})$
Let $G:=\mathrm{GL}_n(\mathbb{R})$ and $f\in C_c^\infty(G)$. One can uniquely determine the Plancherel measure $d\mu_p$ on $\hat{G}$, the unitary (actually tempered) dual of $G$, by the equation
$$f(g …
- 1,692
6
votes
1
answer
124
views
Multi-parameter stationary phase asymptotic expansion
I am looking for an asymptotic expansion of the oscillatory integral of the form
$$\int_{\mathbb{R}^n}f(x)\exp(i(\lambda_1\phi_1(x)+\dots+\lambda_k\phi_k(x))dx,$$
as $\lambda_i\to \infty$ independentl …
- 1,692
3
votes
1
answer
221
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Average size of the Fourier--Stieltjes transform of the fractal measures
For $0<\theta<1/2$ define $\mu_\theta$ to be the uniform (self-similar) measure on the Cantor set obtained from the dissection pattern $(1-2\theta,\theta)$. For example, when $\theta=1/3$ the $\mu_\th …
- 1,692