FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 8, PAGES 3-54

Strongly continuous semigroups of operators generated by systems of pseudodifferential operators in weighted Lp-spaces

K. Kh. Boimatov
I. E. Egorov
M. G. Gadoev

Abstract

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The paper considers semigroups of operators generated by pseudodifferential operators in weighted Lp-spaces of vector functions on Rn (or on a compact manifold without boundary). Sufficient conditions for a semigroup to be strongly continuous and analytic are obtained, conditions for it to be completely continuous are found, and the distribution of the eigenvalues of its infinitesimal generator is examined. Also, an integral representation that singles out the principal term of the semigroup as t ® 0+ is established.

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