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Results tagged with harmonic-analysis
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user 125054
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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Heat equation on torus
Consider heat equation on torus:
$$\partial_tu(x,t) + (- \Delta)^{\alpha/2} u(x,t)=0, u (x, 0)=u_0(x)$$ where $(x, t) \in \mathbb T^d \times \mathbb R, \alpha>0$
Formally, we may write the solution of …
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