Dirichlet-Neumann bracketing for a class of banded Toeplitz matrices
HTML articles powered by AMS MathViewer
- by Martin Gebert PDF
- Proc. Amer. Math. Soc. 150 (2022), 105-117 Request permission
Abstract:
We consider boundary conditions of self-adjoint banded Toeplitz matrices. We ask if boundary conditions exist for banded self-adjoint Toeplitz matrices which satisfy operator inequalities of Dirichlet-Neumann bracketing type. For a special class of banded Toeplitz matrices including integer powers of the discrete Laplacian we find such boundary conditions. Moreover, for this class we give a lower bound on the spectral gap above the lowest eigenvalue.References
- Albrecht Böttcher and Sergei M. Grudsky, Spectral properties of banded Toeplitz matrices, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2005. MR 2179973, DOI 10.1137/1.9780898717853
- M. Gebert and C. Rojas-Molina, Lifshitz tails for random diagonal perturbations of Laurent matrices, preprint, arXiv:2108.03663, 2021.
- Martin Gebert and Constanza Rojas-Molina, Lifshitz tails for the fractional Anderson model, J. Stat. Phys. 179 (2020), no. 2, 341–353. MR 4091563, DOI 10.1007/s10955-020-02533-z
- T. T. Ha and J. A. Gibson, A note on the determinant of a functional confluent Vandermonde matrix and controllability, Linear Algebra Appl. 30 (1980), 69–75. MR 568779, DOI 10.1016/0024-3795(80)90182-2
- Werner Kirsch, An invitation to random Schrödinger operators, Random Schrödinger operators, Panor. Synthèses, vol. 25, Soc. Math. France, Paris, 2008, pp. 1–119 (English, with English and French summaries). With an appendix by Frédéric Klopp. MR 2509110
- Werner Kirsch and Bernd Metzger, The integrated density of states for random Schrödinger operators, Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon’s 60th birthday, Proc. Sympos. Pure Math., vol. 76, Amer. Math. Soc., Providence, RI, 2007, pp. 649–696. MR 2307751, DOI 10.1090/pspum/076.2/2307751
- Michael K. Ng, Raymond H. Chan, and Wun-Cheung Tang, A fast algorithm for deblurring models with Neumann boundary conditions, SIAM J. Sci. Comput. 21 (1999), no. 3, 851–866. MR 1718798, DOI 10.1137/S1064827598341384
- Michael Reed and Barry Simon, Methods of modern mathematical physics. IV. Analysis of operators, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 0493421
- Barry Simon, Lifschitz tails for the Anderson model, J. Statist. Phys. 38 (1985), no. 1-2, 65–76. MR 784931, DOI 10.1007/BF01017848
Additional Information
- Martin Gebert
- Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstraße 39, 80333 München, Germany
- MR Author ID: 1038845
- Email: gebert@math.lmu.de
- Received by editor(s): January 3, 2021
- Received by editor(s) in revised form: May 1, 2021
- Published electronically: October 19, 2021
- Communicated by: Tanya Christiansen
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 105-117
- MSC (2020): Primary 15B05; Secondary 47B35, 34B05
- DOI: https://doi.org/10.1090/proc/15700
- MathSciNet review: 4335861