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Results tagged with fourier-analysis
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user 36735
The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.
1
vote
Accepted
$L^2(X) \cong L^2(X',\xi)$
It is not difficult to see why the maps are inverse to one another, but I am not sure why it is called unfolding. Let $\phi\in L^2(X)$, i.e. $\phi$ is left $A$-invariant. We want to show that
$$\int_{ …
- 1,692
2
votes
0
answers
239
views
Distribution of Fourier coefficients of Maass forms
In the sense of Maass an automorphic function $\phi$ with Laplace-Beltrami eigenvalue $\frac{(d-1)^2}{4}+t^2$ on $d$-dimensional hyperbolic space which can be thought as $\mathbb{R}^{d-1}\times\mathbb …
- 1,692
6
votes
1
answer
124
views
Multi-parameter stationary phase asymptotic expansion
I am looking for an asymptotic expansion of the oscillatory integral of the form
$$\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
views
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