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Subordination in the sense of Bochner of variable order. / Kristian, Evans

Swansea University Author: Kristian, Evans

Abstract

In this thesis we consider subordination (in the sense of Bocnher) of variable order. This work extends previously known results related to operators of variable (fractional) order of differentiation, or variable order fractional powers. The first main result gives a formal backround to the proof th...

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Published: 2008
URI: https://cronfa.swan.ac.uk/Record/cronfa42613
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spelling 2018-08-02T16:24:29.8526076 v2 42613 2018-08-02 Subordination in the sense of Bochner of variable order. cb157aab6ef422edf57a5844c2862452 Kristian Evans Kristian Evans true false 2018-08-02 In this thesis we consider subordination (in the sense of Bocnher) of variable order. This work extends previously known results related to operators of variable (fractional) order of differentiation, or variable order fractional powers. The first main result gives a formal backround to the proof that for certain classes of negative definite symbols q(x,xi) and state space dependent Bernstein functions f(x,s) the pseudo-differential operator -p(x,D) with symbol -f(x,q(x,xi)) extends to the generator of a Feller semigroup. A new concrete example is given. The final result improves upon this result. This is achieved by proving the crucial estimates previously assumed for a large class of symbols and Bernstein functions. EThesis Mathematics. 31 12 2008 2008-12-31 COLLEGE NANME Mathematics COLLEGE CODE Swansea University 2018-08-02T16:24:29.8526076 2018-08-02T16:24:29.8526076 College of Science Mathematics Kristian Evans 1 0042613-02082018162508.pdf 10805371.pdf 2018-08-02T16:25:08.2600000 Output 2085323 application/pdf E-Thesis true 2018-08-02T16:25:08.2600000 false
title Subordination in the sense of Bochner of variable order.
spellingShingle Subordination in the sense of Bochner of variable order.
Kristian, Evans
title_short Subordination in the sense of Bochner of variable order.
title_full Subordination in the sense of Bochner of variable order.
title_fullStr Subordination in the sense of Bochner of variable order.
title_full_unstemmed Subordination in the sense of Bochner of variable order.
title_sort Subordination in the sense of Bochner of variable order.
author_id_str_mv cb157aab6ef422edf57a5844c2862452
author_id_fullname_str_mv cb157aab6ef422edf57a5844c2862452_***_Kristian, Evans
author Kristian, Evans
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hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
department_str Mathematics{{{_:::_}}}College of Science{{{_:::_}}}Mathematics
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description In this thesis we consider subordination (in the sense of Bocnher) of variable order. This work extends previously known results related to operators of variable (fractional) order of differentiation, or variable order fractional powers. The first main result gives a formal backround to the proof that for certain classes of negative definite symbols q(x,xi) and state space dependent Bernstein functions f(x,s) the pseudo-differential operator -p(x,D) with symbol -f(x,q(x,xi)) extends to the generator of a Feller semigroup. A new concrete example is given. The final result improves upon this result. This is achieved by proving the crucial estimates previously assumed for a large class of symbols and Bernstein functions.
published_date 2008-12-31T03:58:09Z
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score 10.900407