Sökning: "Eigenvalues and eigenfunctions"
Visar resultat 1 - 5 av 6 avhandlingar innehållade orden Eigenvalues and eigenfunctions.
1. Heterogeneous Materials - Diffusion, Laplace Spectrum, and Nuclear Magnetic Resonance
Sammanfattning : In this thesis diffusion in heterogeneous materials is studied using spectral analysisof the Laplace operator. Relations to the effective diffusion constant and therelaxation rate of the time-dependent diffusion coefficient for porous systems arederived from the Laplace operator’s spectrum. LÄS MER
2. Some new results concerning general weighted regular Sturm-Liouville problems
Sammanfattning : In this PhD thesis we study some weighted regular Sturm-Liouville problems in which the weight function takes on both positive and negative signs in an appropriate interval [a,b]. With such problems there is the possible existence of non-real eigenvalues, unlike in the definite case (i.e. LÄS MER
3. Trace Formulae for Fourth Order Differential Operators and their Applications
Sammanfattning : Paper I. Trace Formulae and Spectral Properties of FourthOrder Differential Operators.We derive trace formulae forfourth order differential operators in dimension one anddiscuss their connection with sharp Lieb-Thirring inequalitiesfor the Riesz means of negative eigenvalues of order γ≥ 7/4. LÄS MER
4. Spectral estimates for the magnetic Schrödinger operator and the Heisenberg Laplacian
Sammanfattning : I denna avhandling, som omfattar fyra forskningsartiklar, betraktas två operatorer inom den matematiska fysiken. De båda tidigare artiklarna innehåller resultat för Schrödingeroperatorn med Aharonov-Bohm-magnetfält. LÄS MER
5. On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential
Sammanfattning : In this thesis, we generalize a recent result of A. Eremenko and A. Gabrielov on irreducibility of the spectral discriminant for the Schroedinger equation with quartic potentials. LÄS MER