Email this article Dimensions of Solution Spaces of the Schrodinger Equation with Finite Dirichlet Integral on Non-compact Riemannian Manifolds
- Authors: Losev A.G.1, Filatov V.V.1
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Affiliations:
- Volgograd State University
- Issue: Vol 40, No 9 (2019)
- Pages: 1363-1370
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205518
- DOI: https://doi.org/10.1134/S1995080219090142
- ID: 205518
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Abstract
Exact estimations of dimensions of spaces of bounded solutions of stationary Schrodinger equation with finite Dirichlet integral in terms of massive sets are obtained. It is proved that dimension of spaces of bounded solutions of this equation is not less than number of disjoint qD-massive subsets of manifold. This paper partly extends, the results of A.A. Grigor’yan, A.G. Losev (2017).
About the authors
A. G. Losev
Volgograd State University
Author for correspondence.
Email: alexander.losev@volsu.ru
Russian Federation, Volgograd, 400062
V. V. Filatov
Volgograd State University
Author for correspondence.
Email: filatov@volsu.ru
Russian Federation, Volgograd, 400062
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