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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
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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→ R, acting on functions depending on x' ∈ Rn. Further we consider the fractional powers (-A+/-)alp...
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2003
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Institution: | Swansea University |
Degree level: | Doctoral |
Degree name: | Ph.D |
URI: | https://cronfa.swan.ac.uk/Record/cronfa42285 |
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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→ R, acting on functions depending on x' ∈ 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 |
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E-Thesis |
publishDate |
2003 |
institution |
Swansea University |
college_str |
Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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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 |
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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→ R, acting on functions depending on x' ∈ 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 |
2003-12-31T03:52:40Z |
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1763752605475930112 |
score |
11.016235 |