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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
first_indexed 2018-08-02T18:54:20Z
last_indexed 2018-08-03T10:09:44Z
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recordtype RisThesis
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spelling 2018-08-02T16:24:28.6825969 v2 42285 2018-08-02 Some generators of Lp-sub-Markovian semigroups in the half-space R(n+1)/0+. 2c44edee8b82a617e273a64b9617c84e NULL Victoria Knopova Victoria Knopova true true 2018-08-02 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. E-Thesis Mathematics. 31 12 2003 2003-12-31 COLLEGE NANME Mathematics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:28.6825969 2018-08-02T16:24:28.6825969 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Victoria Knopova NULL 1 0042285-02082018162442.pdf 10797993.pdf 2018-08-02T16:24:42.4100000 Output 2710816 application/pdf E-Thesis true 2018-08-02T16:24:42.4100000 false
title Some generators of Lp-sub-Markovian semigroups in the half-space R(n+1)/0+.
spellingShingle Some generators of Lp-sub-Markovian semigroups in the half-space R(n+1)/0+.
Victoria Knopova
title_short Some generators of Lp-sub-Markovian semigroups in the half-space R(n+1)/0+.
title_full Some generators of Lp-sub-Markovian semigroups in the half-space R(n+1)/0+.
title_fullStr Some generators of Lp-sub-Markovian semigroups in the half-space R(n+1)/0+.
title_full_unstemmed Some generators of Lp-sub-Markovian semigroups in the half-space R(n+1)/0+.
title_sort Some generators of Lp-sub-Markovian semigroups in the half-space R(n+1)/0+.
author_id_str_mv 2c44edee8b82a617e273a64b9617c84e
author_id_fullname_str_mv 2c44edee8b82a617e273a64b9617c84e_***_Victoria Knopova
author Victoria Knopova
author2 Victoria Knopova
format E-Thesis
publishDate 2003
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2003-12-31T04:23:14Z
_version_ 1851365570262335488
score 11.089572

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