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Criteria for One‐Sided Invertibility of a Functional Operator in Rearrangement‐Invariant Spaces of Fundamental Type
Author(s) -
Karlovich Alexei Yu.
Publication year - 2001
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(200109)229:1<91::aid-mana91>3.0.co;2-x
Subject(s) - mathematics , invariant (physics) , operator (biology) , pure mathematics , shift operator , diffeomorphism , mathematical analysis , compact operator , mathematical physics , biochemistry , chemistry , repressor , transcription factor , gene , extension (predicate logic) , computer science , programming language
Let γ be a simple open smooth curve and be an orientation‐preserving diffeomorphism of α onto itself which has only two fixed points.Criteria for one‐sided invertibility of thefunctional operator A = aI — bW , where a and b are continuous functions, I is the identity operator, W is the shift operator: ( Wf ) ( t ) = f [ α ( t )], in a reflexive rearrangement‐invariant space of fundamental type X ( γ ) with nontrivial Boyd indices, are obtained.