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| HAL: hal-00725041, version 1 |
| DOI: 10.1007/978-3-0348-0221-5_24 |
| Detailed view |  Export this paper |
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| A panorama of modern operator theory and related topics. The Israel Gohberg memorial volume, Harry Dym, Marinus A. Kaashoek, Peter Lancaster, Heinz Langer and Leonid Lerer (Ed.) (2012) 541-570 |
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| A trace formula for differential operators of arbitrary order |
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| Jörgen Östensson 1Dimitri Yafaev 2 |
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| (2012) |
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| 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. |
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| 1: | Department of Mathematics |
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Uppsala University |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Equations aux dérivées partielles |
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| Subject | : | Mathematics/Analysis of PDEs |
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| One-dimensional differential operators – arbitrary order – resolvents – perturbation determinant – trace formula |
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| hal-00725041, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00725041 | |
| oai:hal.archives-ouvertes.fr:hal-00725041 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Thursday, 23 August 2012 16:47:50 | |
| Updated on: Thursday, 23 August 2012 16:47:50 | |
