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. https://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: | https://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: | 03 Oct 2019 17:55 |
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