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A Panorama of Modern Operator Theory and Related TopicsA Trace Formula for Differential Operators of Arbitrary Order

A Panorama of Modern Operator Theory and Related Topics: A Trace Formula for Differential... [An operator H = H0 +V where H0 = i (N is arbitrary) and V is a differential operator of order N-1 with coefficients decaying sufficiently rapidly at infinity is considered in the space H2(R). The goal of the paper is to find an expression for the trace of the difference of the resolvents (H) -1 and (H0 - z) -1 in terms of the Wronskian of appropriate solutions to the differential equation Hu = zu. This also leads to a representation for the perturbation determinant of the pair H0H.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Panorama of Modern Operator Theory and Related TopicsA Trace Formula for Differential Operators of Arbitrary Order

Part of the Operator Theory: Advances and Applications Book Series (volume 218)
Editors: Dym, Harry; Kaashoek, Marinus A.; Lancaster, Peter; Langer, Heinz; Lerer, Leonid
Östensson, J.; Yafaev, D. R.
A Panorama of Modern Operator Theory and Related Topics — Jan 3, 2012
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Publisher
Springer Basel
Copyright
© Springer Basel AG 2012
ISBN
978-3-0348-0220-8
Pages
541 –570
DOI
10.1007/978-3-0348-0221-5_24
Publisher site
See Chapter on Publisher Site

Abstract

[An operator H = H0 +V where H0 = i (N is arbitrary) and V is a differential operator of order N-1 with coefficients decaying sufficiently rapidly at infinity is considered in the space H2(R). The goal of the paper is to find an expression for the trace of the difference of the resolvents (H) -1 and (H0 - z) -1 in terms of the Wronskian of appropriate solutions to the differential equation Hu = zu. This also leads to a representation for the perturbation determinant of the pair H0H.]

Published: Jan 3, 2012

Keywords: One-dimensional differential operators; arbitrary order; resolvents; perturbation determinant; trace formula

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