Robert S. Strichartz

TL;DR: In this paper, the authors give a complete solution when S is a quadratic surface given by the duality argument for the special case S {(x, y) yZ xz I} and give the interpretation of the answer as a space-time decay for solutions of the Klein-Gordon equation with finite relativistic invariant norm.

TL;DR: In this paper, it was shown that the classical theory of he Laplacian remains valid for the Laplace-Beltrami operator on a complete Riemannian manifold.

TL;DR: In this paper, the authors provide a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. But they do not consider the application of Fourier transform in the field of physics.

TL;DR: From Manifolds to Fractals Analysis on manifolds has been one of the central areas of mathematical research in the twentieth century as discussed by the authors, and it has attracted mathematicians with diverse expertise and points of view, including topology, differential equations, differential geometry, functional and harmonic analysis and probability theory.