English

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

Analysis of PDEs 2007-05-23 v1 Functional Analysis

Abstract

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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Cite

@article{arxiv.math/9909139,
  title  = {The Method of Ascent and cos(sqrt(A^2+b^2))},
  author = {Yakar Kannai},
  journal= {arXiv preprint arXiv:math/9909139},
  year   = {2007}
}

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