Sökning: "Singular Operators"
Visar resultat 1 - 5 av 23 avhandlingar innehållade orden Singular Operators.
1. Studies of some Operators of Harmonic Analysis in certain Function Spaces with Applications to PDEs
Sammanfattning : The study in this PhD thesis aims at development of certain mathematical methods used in applications, in particular, in the study of regularity properties of solutions in various mathematical models described by Partial Differential Equations (PDEs). To this end, we study various operators of harmonic analysis in certain function spaces, since solutions to many PDEs may be expressed in terms of such operators. LÄS MER
2. Spectra of elliptic operators and applications
Sammanfattning : In this thesis we consider several problems related to elliptic equations. Namely, we investigate Helmholtz and Maxwell's equations in Paper I and Sturm-Liouville spectral problem in Papers II,III. In Paper I we study time-harmonic electromagnetic and acoustic waveguide, modeled by an in�nite cylinder with a non-smooth cross section. LÄS MER
3. On Vertex Operator Algebras of Affine Type at Admissible Levels
Sammanfattning : The main purpose of this thesis is the study of the structure and representation theory of simple vertex operator algebras (VOAs) of affine type at admissible levels. To do this, it is crucial to obtain knowledge of the singular vectors which generate the maximal submodules, with respect to which these VOAs appear as irreducible quotients, and therefore a substantial part of the text is devoted to this matter. LÄS MER
4. Inverse Problems in Tomography and Fast Methods for Singular Convolutions
Sammanfattning : There are two, partially interlaced, themes treated in this thesis; inverse problems of tomographic type and fast and accurate methods for the application of convolution operators. Regarding the first theme, the inverse problem of Doppler tomography is considered and the Doppler moment transform is introduced for that purpose. LÄS MER
5. Spectral properties of elliptic operators in singular settings and applications
Sammanfattning : The present thesis is focused on the investigation of the spectral properties of the linear elliptic operators in the presence of singularities. It is divided into three chapters. In the first chapter, we consider geometric singularities. LÄS MER