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Taylor coefficients of a pseudo‐exponential potential and the reflection coefficient of the corresponding canonical system
Author(s) -
Gohberg I.,
Kaashoek M. A.,
Sakhnovich A. L.
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310323
Subject(s) - mathematics , exponential function , taylor series , zero (linguistics) , reflection coefficient , reflection (computer programming) , mathematical analysis , connection (principal bundle) , geometry , physics , optics , philosophy , linguistics , computer science , programming language
We study the connections between the Taylor coefficients at zero of a pseudo‐exponential potential of a canonical system and the reflection coefficient of the system determined by this potential. This connection is expressed explicitly. The main result of this paper provides a characterization of a pseudo‐exponential potential in terms of its Taylor coefficients at zero. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)