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Picard Operators
Author(s) -
Weikard Rudi
Publication year - 1998
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.19981950114
Subject(s) - mathematics , pure mathematics , meromorphic function , expression (computer science) , differential operator , spectrum (functional analysis) , mathematical analysis , physics , quantum mechanics , computer science , programming language
A linear differential expression Ly = y (n) + qn ‐2 y n‐2 +…+ q 0 y is called a Picard expression if its coefficients are elliptic functions (with common fundamental periods) and if the general solution of Ly = Ey is an everywhere meromorphic function (with respect to the independent variable) for all E ∈ ℂ. If L is a Picard expression we show that the differential equation Ly = Ey has n linearly independent Floquet solutions except when E is any of a finite number of exceptional values. Also the conditional stability set of a Picard expression (and hence the spectrum of the associated operator in L 2 (ℝ)) consists of finitely many regular analytic arcs.