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Results tagged with harmonic-analysis
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user 171439
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.
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Beltrami equation with harmonic coefficient
I need to find solutions to the Beltrami equation
$$
\frac{\partial w}{\partial\overline{{z}}}=e^{i\varphi(z)}\frac{\partial w}{\partial z}
$$
for $w=w(z,\overline{z})$ and $\varphi(z)$ some given, r …
- 134
1
vote
Accepted
Linear elliptic equation
The equation is happily linear, so depending on the domain you may find separable analytical solutions to the Dirichlet problem thanks to Sturm–Liouville.
For instance, let's take the domain to be a u …
- 134