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Direct and Inverse Scattering Problem for Canonical Systems with a Strictly Pseudo – Exponential Potential
Author(s) -
Alpay D.,
Gohberg I.,
Kaashoek M.A.,
Sakhnovich A.L.
Publication year - 2000
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 - 10.1002/1522-2616(200007)215:1<5::aid-mana5>3.0.co;2-m
Subject(s) - mathematics , mathematical proof , inverse scattering problem , exponential function , inverse , canonical form , matrix (chemical analysis) , scattering theory , inverse problem , function (biology) , pure mathematics , algebra over a field , scattering , mathematical analysis , quantum mechanics , materials science , geometry , physics , composite material , evolutionary biology , biology
Explicit formulas are given for the solutions of the direct and inverse scattering problems for a canonical differential system with a strictly pseudo–exponential potential. The proofs are self–contained and employ state space techniques from mathematical system theory. The paper supplements an earlier paper of the first two authors where explicit formulas were given using Marchenko's approach, and an earlier paper of the last three authors where self–contained proofs were given for the corresponding direct and inverse spectral problems. Two types of factorizations of the scattering matrix function appear and connections between them are considered.