The Method of Ascent and cos(sqrt(A^2+b^2))

Details The Method of Ascent and cos(sqrt(A^2+b^2)) The Method of Ascent and cos(sqrt(A^2+b^2))

1999-09-23

arxiv.org/abs/math/9909139v1

Mathematics

Analysis of PDEs

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Scientific paper

The fundamental solution for the wave equation in n variables is built from the simple one-dimensional formula, via an integral representation of the cosine of the sum of squares of self-adjoint operators. Representation formulas are given both in the commutative and non-commutative case. The formulas are illustrated for the wave equation as well as for the Klein-Gordon equati on. As examples for the non-commuting case, we discuss the harmonic oscillator and simple sum of squares hypoelliptic operators such as the Grushin operator and the Heisenberg Laplacian.

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