Hierarchical Schrödinger Operators with Singular Potentials
Bendikov A, Grigoryan A, Molchanov S (2023)
Proceedings of the Steklov Institute of Mathematics 323(1): 12-46.
Zeitschriftenaufsatz
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Autor*in
Bendikov, Alexander;
Grigoryan, AlexanderUniBi;
Molchanov, Stanislav
Einrichtung
Abstract / Bemerkung
We consider the operator H=L+V that is a perturbation of the Taibleson-Vladimirov operator L=D(alpha )by a potential V(x)=b & Vert;x & Vert;(-alpha),where alpha>0 and b >= b(& lowast;).Weprove that the operator H is closable and its minimal closure is a nonnegative definite self-adjoint operator (where the critical value b(& lowast;)depends on alpha). While the operator H is nonnegative definite, the potential V(x) may well take negative values as b(& lowast;)<0 for all 0
Stichworte
ultrametric space;
-adic numbers;
Dyson model;
hierarchical Laplacian;
hierarchical Schrodinger operator;
Vladimirov operator
Erscheinungsjahr
2023
Zeitschriftentitel
Proceedings of the Steklov Institute of Mathematics
Band
323
Ausgabe
1
Seite(n)
12-46
ISSN
0081-5438
eISSN
1531-8605
Page URI
https://pub.uni-bielefeld.de/record/2987948
Zitieren
Bendikov A, Grigoryan A, Molchanov S. Hierarchical Schrödinger Operators with Singular Potentials. Proceedings of the Steklov Institute of Mathematics. 2023;323(1):12-46.
Bendikov, A., Grigoryan, A., & Molchanov, S. (2023). Hierarchical Schrödinger Operators with Singular Potentials. Proceedings of the Steklov Institute of Mathematics, 323(1), 12-46. https://doi.org/10.1134/S0081543823050024
Bendikov, Alexander, Grigoryan, Alexander, and Molchanov, Stanislav. 2023. “Hierarchical Schrödinger Operators with Singular Potentials”. Proceedings of the Steklov Institute of Mathematics 323 (1): 12-46.
Bendikov, A., Grigoryan, A., and Molchanov, S. (2023). Hierarchical Schrödinger Operators with Singular Potentials. Proceedings of the Steklov Institute of Mathematics 323, 12-46.
Bendikov, A., Grigoryan, A., & Molchanov, S., 2023. Hierarchical Schrödinger Operators with Singular Potentials. Proceedings of the Steklov Institute of Mathematics, 323(1), p 12-46.
A. Bendikov, A. Grigoryan, and S. Molchanov, “Hierarchical Schrödinger Operators with Singular Potentials”, Proceedings of the Steklov Institute of Mathematics, vol. 323, 2023, pp. 12-46.
Bendikov, A., Grigoryan, A., Molchanov, S.: Hierarchical Schrödinger Operators with Singular Potentials. Proceedings of the Steklov Institute of Mathematics. 323, 12-46 (2023).
Bendikov, Alexander, Grigoryan, Alexander, and Molchanov, Stanislav. “Hierarchical Schrödinger Operators with Singular Potentials”. Proceedings of the Steklov Institute of Mathematics 323.1 (2023): 12-46.
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