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E-Thesis 66 views 38 downloads

Some generators of Lp-sub-Markovian semigroups in the half-space R(n+1)/0+. / Victoria Knopova

Swansea University Author: Victoria Knopova

Abstract

In this thesis we study pseudo-differential operators of the form [mathematical equation] where psi(Dx') is an operator with real continuous negative definite symbol psi: Rn→ R, acting on functions depending on x' ∈ Rn. Further we consider the fractional powers (-A+/-)alp...

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Published: 2003
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42285
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Abstract: In this thesis we study pseudo-differential operators of the form [mathematical equation] where psi(Dx') is an operator with real continuous negative definite symbol psi: Rn&rarr; R, acting on functions depending on x' &isin; Rn. Further we consider the fractional powers (-A+/-)alpha 0 < alpha < 1, of -A+/-. After determining the domains in Lp(R(n+1)/0+) of these operators in terms of Bessel-type potential spaces and studying some properties of these function spaces, we prove that with these domains -(-A+/-)alpha are generators of Lp-sub- Markovian semigroups. Then we extend this result and show that the operators --(--A+/-)alpha -- p(x', Dx') also generate Lp-sub-Markovian semigroups, if the pseudo-differential operator p(x', Dx') is (-A+/-)alpha-bounded and the symbol p(x', xi') of p(x',Dx') is with respect to a continuous negative definite function. In the end we proved the continuity of the pseudo-differential operator with continuous negative definite symbol (with certain condition on the growth of the Levy measure) between the Besov spaces.
Keywords: Mathematics.
College: College of Science