Abstract
The article is devoted to the construction of the exponential function of the matrix pseudo-differential operator, which does not satisfy conditions of any known theorem (see, e.g. Sec. 8 Ch. VIII and Sec. 2 Ch. XI of Treves in Introduction to the theory of pseudodifferential and Fourier integral operator, vols. 1 & 2, Plenum Press, New York, 1980). An application of the exponential function to the fundamental solution of the Cauchy problem for the hyperbolic operators with the characteristics of variable multiplicity is given.
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Dedicated to Professor Kunihiko Kajitani on the occasion of his 70th birthday
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Galstian, A. Exponential Function of Pseudo-Differential Operators in Gevrey Spaces. Integr. Equ. Oper. Theory 70, 281–300 (2011). https://doi.org/10.1007/s00020-010-1850-3
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DOI: https://doi.org/10.1007/s00020-010-1850-3