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Roth's method and the Yosida approximation for pseudodifferential operators with negative definite symbols. / Alexander Potrykus

Swansea University Author: Alexander Potrykus

Abstract

This thesis consists of two parts. The first one extends an idea developed by J.P. Roth. He succeeded to construct a Feller semigroup associated with a second order elliptic differential operator L(x D) by investigating the semigroups obtained by freezing the coefficients of L(xD). In Chapter 2 we s...

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Published: 2005
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42468
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first_indexed 2018-08-02T18:54:47Z
last_indexed 2018-08-03T10:10:14Z
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spelling 2018-08-02T16:24:29.3533874 v2 42468 2018-08-02 Roth's method and the Yosida approximation for pseudodifferential operators with negative definite symbols. 8fa0ebf5323b17237018f4c4b36f4de9 NULL Alexander Potrykus Alexander Potrykus true true 2018-08-02 This thesis consists of two parts. The first one extends an idea developed by J.P. Roth. He succeeded to construct a Feller semigroup associated with a second order elliptic differential operator L(x D) by investigating the semigroups obtained by freezing the coefficients of L(xD). In Chapter 2 we show that a modification of his method works also for certain pseudodifferential operators with bounded negative definite symbols. Partly we can rely on ideas of E. Popescu. In Chapter 3 we show that if a certain pseudodifferential operator -q(xD) generates a Feller semigroup (Tt)t&ge;0 then the Feller semigroups (Tt([v]))t&ge;0 generated by the pseudodifferential operators whose symbols are the Yosida approximations of -q(x,xi)i.e. [formula] converge strongly to (Tt(v))t&ge;0. E-Thesis Mathematics. 31 12 2005 2005-12-31 COLLEGE NANME Mathematics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:29.3533874 2018-08-02T16:24:29.3533874 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Alexander Potrykus NULL 1 0042468-02082018162456.pdf 10798176.pdf 2018-08-02T16:24:56.8730000 Output 2636674 application/pdf E-Thesis true 2018-08-02T16:24:56.8730000 false
title Roth's method and the Yosida approximation for pseudodifferential operators with negative definite symbols.
spellingShingle Roth's method and the Yosida approximation for pseudodifferential operators with negative definite symbols.
Alexander Potrykus
title_short Roth's method and the Yosida approximation for pseudodifferential operators with negative definite symbols.
title_full Roth's method and the Yosida approximation for pseudodifferential operators with negative definite symbols.
title_fullStr Roth's method and the Yosida approximation for pseudodifferential operators with negative definite symbols.
title_full_unstemmed Roth's method and the Yosida approximation for pseudodifferential operators with negative definite symbols.
title_sort Roth's method and the Yosida approximation for pseudodifferential operators with negative definite symbols.
author_id_str_mv 8fa0ebf5323b17237018f4c4b36f4de9
author_id_fullname_str_mv 8fa0ebf5323b17237018f4c4b36f4de9_***_Alexander Potrykus
author Alexander Potrykus
author2 Alexander Potrykus
format E-Thesis
publishDate 2005
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 This thesis consists of two parts. The first one extends an idea developed by J.P. Roth. He succeeded to construct a Feller semigroup associated with a second order elliptic differential operator L(x D) by investigating the semigroups obtained by freezing the coefficients of L(xD). In Chapter 2 we show that a modification of his method works also for certain pseudodifferential operators with bounded negative definite symbols. Partly we can rely on ideas of E. Popescu. In Chapter 3 we show that if a certain pseudodifferential operator -q(xD) generates a Feller semigroup (Tt)t&ge;0 then the Feller semigroups (Tt([v]))t&ge;0 generated by the pseudodifferential operators whose symbols are the Yosida approximations of -q(x,xi)i.e. [formula] converge strongly to (Tt(v))t&ge;0.
published_date 2005-12-31T03:53:01Z
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score 10.998321

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