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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...

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Published: 2008
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42613
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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.
Keywords: Mathematics.
College: College of Science