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
$L$**_{p}-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 $L$_{p}-spaces of
vector functions on $$**R**^{n}
(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.

Location: http://mech.math.msu.su/~fpm/eng/k08/k088/k08801h.htm

Last modified: October 18, 2009