Search for dissertations about: "Potential Operators"

Showing result 1 - 5 of 145 swedish dissertations containing the words Potential Operators.

2. 1. Studies of some Operators of Harmonic Analysis in certain Function Spaces with Applications to PDEs

   Author : Staffan Lundberg; Norway Narvik UiT The Arctic University of Norway Department of Computer Science and Computational Engineering Faculty of Science and Technology; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Operators; Hardy Operators; Potential Operators; Singular Operators; Function Spaces; Morrey Spaces; H¨older Spaces; Partial Differential Equations; Inequalities; Hardy Type Inequalities; Weights; Applications; Matematik; Mathematics;

   Abstract : 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. READ MORE

4. 2. Resolvent Estimates and Bounds on Eigenvalues for Schrödinger and Dirac Operators

   Author : Alexandra Enblom; Vladimir Kozlov; Ari Laptev; David Krejcirik; Linköpings universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Spectral theory; Schrödinger operators; polyharmonic operators; Dirac operators; non-self-adjoint perturbations; complex potential; estimation of eigenvalues; Carleman inequalities; Hardy inequalities;

   Abstract : This thesis concerns the spectral theory of Schrödinger and Dirac operators. The main results relate to the problems of estimating perturbed eigenvalues. The thesis is based on four papers.The first paper focuses on the problem of localization of perturbed eigenvalues for multidimensional Schrödinger operators. READ MORE

5. 3. Schrödinger Operators in Waveguides

   Author : Tomas Ekholm; Timo Weidl; Ari Laptev; Pavel Exner; KTH; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Schrödinger Operators; Hardy Inequalities; Mathematical physics; Matematisk fysik;

   Abstract : In this thesis, which consists of four papers, we study the discrete spectrum of Schrödinger operators in waveguides. In these domains the quadratic form of the Dirichlet Laplacian operator does not satisfy any Hardy inequality. READ MORE

6. 4. Resonances of Dirac Operators

   Author : Jimmy Kungsman; Wolfgang Staubach; Roman Schubert; Uppsala universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Semiclassical analysis; Dirac operator; resonances; Poisson trace formula; scattering theory; complex absorbing potential; pseudodifferential operator; Mathematics; Matematik;

   Abstract : This thesis consists of a summary of four papers dealing with resonances of Dirac operators on Euclidean 3-space. In Paper I we show that the Complex Absorbing Potential (CAP) method is valid in the semiclassical limit for resonances sufficiently close to the real line if the potential is smooth and compactly supported. READ MORE

7. 5. Spectra of elliptic operators and applications

   Author : Medet Nursultanov; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Helmholtz and Maxwell s equations; functional calculus; electromagnetic waveguide; acoustic waveguide; Sturm-Liouville operator; singular potential; asymptotics of eigenvalues; point interactions.;

   Abstract : 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. READ MORE