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The fractional Schrödinger operator and Toeplitz matrices

J. Math. Phys. 50, 103524 (2009); doi:10.1063/1.3237146

Published 9 October 2009

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Agapitos Hatzinikitas
Department of Mathematics, School of Sciences, University of Aegean, Karlovasi, 83200 Samos, Greece
Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schödinger operator with the truncated Toeplitz matrices. We determine the asymptotic behavior of the product of eigenvalues for the alpha-stable symmetric laws by employing the Szegö's strong limit theorem. The results of the present work can be applied to a recently proposed model for a particle hopping on a bounded interval in one dimension whose hopping probability is given a discrete representation of the fractional Laplacian. ©2009 American Institute of Physics
History: Received 12 January 2009; accepted 31 August 2009; published 9 October 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/103524/1
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ISSN:
0022-2488 (print)   1089-7658 (online)
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