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A trace formula for differential operators of arbitrary order
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2012 (English)In: A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial Volume / [ed] Harry Dym, Marinus A. Kaashoek, Peter Lancaster, Heinz Langer & Leonid Lerer, Basel: Birkhäuser Verlag, 2012, Vol. 218, p. 541-570Chapter in book (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Basel: Birkhäuser Verlag, 2012. Vol. 218, p. 541-570
Series
Operator Theory: Advances and Applications, ISSN 0255-0156, E-ISSN 2296-4878 ; 218
Keywords [en]
One-dimensional differential operators, arbitrary order, resolvents, perturbation determinant, trace formula
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-293567DOI: 10.1007/978-3-0348-0221-5_24ISBN: 978-3-0348-0220-8 (print)ISBN: 978-3-0348-0789-0 (print)ISBN: 978-3-0348-0221-5 (electronic)OAI: oai:DiVA.org:uu-293567DiVA, id: diva2:927990
Available from: 2016-05-13 Created: 2016-05-13 Last updated: 2022-10-04Bibliographically approved

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Östensson, Jörgen

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Output format
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