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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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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 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≥0 then the Feller semigroups (Tt([v]))t≥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≥0.
Keywords: Mathematics.
College: Faculty of Science and Engineering