Wavelet Frames,Sobolev Embeddings and Negative Spectrum of Schrödinger Operators on Manifolds with Bounded Geometry |
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Authors: | Leszek Skrzypczak |
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Institution: | (1) Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland |
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Abstract: | We consider weighted function spaces of Sobolev-Besov type and Schrödinger type operators on noncompact Riemannian manifolds with bounded geometry. First we give characterization of the spaces in terms of wavelet frames. Then we describe the necessary and sufficient conditions for the compactness of Sobolev embeddings between the spaces. An asymptotic behavior of the corresponding entropy numbers is calculated. At the end we use the asymptotic behavior to estimate the number of negative eigenvalues of the Schrödinger type operators. |
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Keywords: | Weighted Sobolev and Besov spaces Wavelet frames Compact embeddings Entropy numbers Schr?dinger operators Negative spectrum |
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