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Sectorial Stieltjes functions and their realizations by L‐systems with a Schrödinger operator
Author(s) -
Belyi Sergey
Publication year - 2012
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.201100226
Subject(s) - mathematics , operator (biology) , schrödinger's cat , riemann–stieltjes integral , class (philosophy) , state (computer science) , shift operator , function (biology) , space (punctuation) , state space , mathematical analysis , function space , multiplication operator , pure mathematics , compact operator , hilbert space , algorithm , integral equation , extension (predicate logic) , computer science , repressor , artificial intelligence , chemistry , biology , biochemistry , evolutionary biology , transcription factor , programming language , statistics , gene , operating system
We consider classes of sectorial Stieltjes functions. It is shown that a function belonging to these classes can be realized as the impedance function of a singular L‐system with a sectorial state‐space operator. We provide an additional condition on a given function from this class so that the state‐space operator of the realizing L‐system is α‐sectorial with the exact angle of sectoriality α. Then these results are applied to L‐systems based upon a non‐self‐adjoint Schrödinger operator.