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Results tagged with laplacian
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user 56624
The Laplacian matrix is the representation of a graph in matrix form.
5
votes
Accepted
Poisson summation formula and its implication for the spectrum of the flat torus
The theta function (the left-hand side of the Jacobi identity) uniquely determines the values of ${||\gamma^*||:\gamma^*\in\Gamma^*}$ counted with multiplicities, just by looking inductively at its as …
- 8,992
17
votes
Why decompose a function with eigenvectors of Laplace operator?
The exponentials used in Fourier series are eigenvalues of shifts, and thus of any operator commuting with shifts, not just Laplacian. …
- 8,992
6
votes
Accepted
Fundamental solution of Discrete Laplace in the plane
For nearest neighbor Laplacian, you can find a short self-contained proof of the formula $$u(x)=\frac1{2\pi}\log |x|+c+O\left(\frac1{|x|^2}\right)$$ at these lecture notes, pages 6-7. … The proof there is not the shortest possible; the easiest way would be to compare the double integral formula defining $G_0$ on page 6 with its counterpart for continuous Laplacian. …
- 8,992