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A Cayley-Hamiltonian Theorem for Periodic Finite Band Matrices

Simon, Barry (2017) A Cayley-Hamiltonian Theorem for Periodic Finite Band Matrices. In: Functional analysis and operator theory for quantum physics : Pavel Exner anniversary volume. EMS Publishing House , Zurich, Switzerland, pp. 525-529. ISBN 978-3-03719-175-0.

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Let K be a doubly infinite, self-adjoint matrix which is finite band (i.e. K_(jk) = 0 if |j – k| > m) and periodic (K S^n = S^n K for some n where (Su)_j = u_(j+1)) and non-degenerate (i.e. K_(jj+m) ≠ = 0 for all j). Then, there is a polynomial, p(x, y), in two variables with p(K, S^n) = 0. This generalizes the tridiagonal case where p(x, y) = y^2 - yΔ(x) + 1 where Δ is the discriminant. I hope Pavel Exner will enjoy this birthday bouquet.

Item Type:Book Section
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Simon, Barry0000-0003-2561-8539
Additional Information:© 2017 EMS Publishing House. Research supported in part by NSF grant DMS-1265592 and in part by Israeli BSF Grant No. 2014337.
Funding AgencyGrant Number
Binational Science Foundation (USA-Israel)2014337
Subject Keywords:Periodic Jacobi Matrices, Discriminant, Magic Formula
Classification Code:2010 Mathematics Subject Classification. Primary 47B36, 47B39, 30C10
Record Number:CaltechAUTHORS:20170508-161208689
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77271
Deposited By: Tony Diaz
Deposited On:16 May 2017 20:44
Last Modified:15 Nov 2021 17:29

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