No Cover Image

E-Thesis 29 views 3 downloads

Subordination in the sense of Bochner of variable order. /

Swansea University Author: Evans, Kristian

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...

Full description

Published: 2008
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42613
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2018-08-02T18:55:07Z
last_indexed 2018-08-03T10:10:37Z
id cronfa42613
recordtype RisThesis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2018-08-02T16:25:08Z</datestamp><bib-version>v2</bib-version><id>42613</id><entry>2018-08-02</entry><title>Subordination in the sense of Bochner of variable order.</title><alternativeTitle></alternativeTitle><author>Kristian Evans</author><firstname>Kristian</firstname><surname>Evans</surname><active>true</active><ORCID/><ethesisStudent>true</ethesisStudent><sid>d3c071e057db0e30697060acadea9763</sid><email>b7620342928f2a7f5868b7f09c4f8cc5</email><emailaddr>qAC8Xkb4k4bZ6FKXKDt9Z9yvqZQRJmUl2lxhnzSZE7o=</emailaddr><date>2018-08-02</date><deptcode>SMA</deptcode><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 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.</abstract><type>E-Thesis</type><journal></journal><volume/><journalNumber></journalNumber><paginationStart></paginationStart><paginationEnd></paginationEnd><publisher></publisher><placeOfPublication></placeOfPublication><isbnPrint></isbnPrint><isbnElectronic/><issnPrint></issnPrint><issnElectronic></issnElectronic><keywords>Mathematics.</keywords><publishedDay>0</publishedDay><publishedMonth>0</publishedMonth><publishedYear>2008</publishedYear><publishedDate>2008-01-01</publishedDate><doi></doi><url></url><notes></notes><college>College of Science</college><department>Mathematics</department><CollegeCode>CSCI</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><researchGroup></researchGroup><supervisor></supervisor><sponsorsfunders/><grantnumber/><degreelevel>Doctoral</degreelevel><degreename>Ph.D</degreename><lastEdited>2018-08-02T16:24:29Z</lastEdited><Created>2018-08-02T16:24:29Z</Created><path><level id="1">College of Science</level><level id="2">Mathematics</level></path><authors/><documents><document><filename>0042613-02082018162508.pdf</filename><originalFilename>10805371.pdf</originalFilename><uploaded>2018-08-02T16:25:08Z</uploaded><type>Output</type><contentLength>123456</contentLength><contentType>application/pdf</contentType><version>E-Thesis</version><cronfaStatus>true</cronfaStatus><action>Published to Cronfa</action><actionDate>02/08/2018</actionDate><embargoDate>2018-08-02T16:25:08.26</embargoDate><documentNotes/><copyrightCorrect>false</copyrightCorrect><language/></document></documents></rfc1807>
spelling 2018-08-02T16:25:08Z v2 42613 2018-08-02 Subordination in the sense of Bochner of variable order. Kristian Evans Kristian Evans true true d3c071e057db0e30697060acadea9763 b7620342928f2a7f5868b7f09c4f8cc5 qAC8Xkb4k4bZ6FKXKDt9Z9yvqZQRJmUl2lxhnzSZE7o= 2018-08-02 SMA 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. E-Thesis Mathematics. 0 0 2008 2008-01-01 College of Science Mathematics CSCI SMA Swansea University Doctoral Ph.D 2018-08-02T16:24:29Z 2018-08-02T16:24:29Z College of Science Mathematics 0042613-02082018162508.pdf 10805371.pdf 2018-08-02T16:25:08Z Output 123456 application/pdf E-Thesis true Published to Cronfa 02/08/2018 2018-08-02T16:25:08.26 false
title Subordination in the sense of Bochner of variable order.
spellingShingle Subordination in the sense of Bochner of variable order.
Evans, Kristian
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 d3c071e057db0e30697060acadea9763
author_id_fullname_str_mv d3c071e057db0e30697060acadea9763_***_Evans, Kristian
author Evans, Kristian
author2
format E-Thesis
publishDate 2008
institution Swansea University
college_str College of Science
hierarchytype
hierarchy_top_id collegeofscience
hierarchy_top_title College of Science
hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
department_str Mathematics{{{_:::_}}}College of Science{{{_:::_}}}Mathematics
document_store_str 1
active_str 1
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 2008-01-01T05:10:08Z
_version_ 1647521571821060096
score 10.859247