Search for dissertations about: "Ari Laptev"
Showing result 1 - 5 of 9 swedish dissertations containing the words Ari Laptev.
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1. Hardy and spectral inequalities for a class of partial differential operators
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
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2. Improved Lp Hardy Inequalities
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
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3. Asymptotic and universal spectral estimates with applications in many-body quantum mechanics and spectral shape optimization
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
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4. Schrödinger Operators in Waveguides
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
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5. Properties of the Discrete and Continuous Spectrum of Differential Operators
Abstract : This thesis contains three scientific papers devoted to the study of different spectral theoretical aspects of differential operators in Hilbert spaces.The first paper concerns the magnetic Schrödinger operator (i∇ + A)2 in L2(ℝn). READ MORE