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.
http://resolver.caltech.edu/CaltechAUTHORS:20170508-161208689

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## Abstract

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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Additional Information: | © 2017 EMS Publishing House. Research supported in part by NSF grant DMS-1265592 and in part by Israeli BSF Grant No. 2014337. | |||||||||

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Subject Keywords: | Periodic Jacobi Matrices, Discriminant, Magic Formula | |||||||||

Classification Code: | 2010 Mathematics Subject Classification. Primary 47B36, 47B39, 30C10 | |||||||||

Record Number: | CaltechAUTHORS:20170508-161208689 | |||||||||

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20170508-161208689 | |||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||

ID Code: | 77271 | |||||||||

Collection: | CaltechAUTHORS | |||||||||

Deposited By: | Tony Diaz | |||||||||

Deposited On: | 16 May 2017 20:44 | |||||||||

Last Modified: | 08 Jan 2018 17:05 |

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