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Convolution groups for quasihyperbolic systems of differential operators


Abstract


In contrast to the usual treatment (see e.g. J.J. Duistermaat [3]) convolution groups are constructed for differential operators defined by non-homogeneous polynomials (Proposition 5) and for quasi-hyperbolic systems, i.e. systems "correct in the sense of Petrovsky" (Proposition 9). An explicit formula for the convolution group of the Lame system in elastodynamics is presented in Proposition 11.

DOI Code: 10.1285/i15900932v25n2p139

Keywords: Fundamental solutions; Fundamental matrices; Convolution of distributions

Classification: 35E05; 35E20; 35K25; 46F12; 74H05

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