Search for dissertations about: "spectral inequalities"

Showing result 1 - 5 of 12 swedish dissertations containing the words spectral inequalities.

  2. 1. Spectral Inequalities and Their Applications in Quantum Mechanics

    Author : Fabian Portmann; Ari Laptev; Robert Seiringer; KTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Spectral inequalities; quantum mechanics; Hardy inequalities; Sobolev inequalities; Lieb-Thirring inequalities; stability of matter; Bose gases; Bose-Einstein condensation; Mathematics; Matematik; Fysik; Physics;

    Abstract : The work presented in this thesis revolves around spectral inequalities and their applications in quantum mechanics.In Paper A, the ground state energy of an atom confined to two dimensions is analyzed in the limit when the charge of the nucleus Z becomes very large. READ MORE

  4. 2. Asymptotic and universal spectral estimates with applications in many-body quantum mechanics and spectral shape optimization

    Author : Simon Larson; Ari Laptev; Stefan Steinerberger; KTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Spectral theory; shape optimization; semiclassical asymptotics; spectral inequalities; quantum mechanics; Mathematics; Matematik;

    Abstract : This thesis consists of eight papers primarily concerned with the quantitative study of the spectrum of certain differential operators. The majority of the results split into two categories. READ MORE

  5. 3. Improved Lp Hardy Inequalities

    Author : Jesper Tidblom; Ari Laptev; Andrzej Szulkin; Achilles Tertikas; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Spectral theory; Hardy inequality; MATHEMATICS; MATEMATIK;

    Abstract : Paper 1 : A geometrical version of Hardy's inequality for W_0^{1,p}(D).The aim of this article is to prove a Hardy-type inequality, concerning functions in W_0^{1,p}(D) for some domain D in R^n, involving the volume of D and the distance to the boundary of D. The inequality is a generalization of a previously proved inequality by M. and T. READ MORE

  6. 4. 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

  7. 5. Hardy and spectral inequalities for a class of partial differential operators

    Author : Lior Alexandra Aermark; Ari Laptev; Thomas Hoffmann-Ostenhof; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Mathematics; matematik;

    Abstract : This thesis is devoted to the study of Hardy and spectral inequalities for the Heisenberg and the Grushin operators. It consists of five chapters. In chapter 1 we present basic notions and summarize the main results of the thesis. READ MORE