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On the Characterization of the Intermediate Space in Generalized Factorizations
Author(s) -
Castro L. P.,
Speck F.O.
Publication year - 1995
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.19951760104
Subject(s) - mathematics , eigenvalues and eigenvectors , pure mathematics , factorization , bounded function , invariant (physics) , operator (biology) , algebra over a field , partial fraction decomposition , mathematical analysis , biochemistry , chemistry , physics , algorithm , quantum mechanics , repressor , transcription factor , mathematical physics , gene , rational function
The study of systems of singular integral equations of C AUCHY type, of T OEPLITZ and W IENER ‐H OPF operators leads to the question of existence and representation of generalized factorizations of matrix functions Φ in [ L P (Γ, σ)] m . This yields a corresponding factorization of the basic multiplication or translation invariant operator A = A _ CA + , respectively, which can be seen as a splitting of a bounded into unbounded operators. The present paper is devoted to the study of the nature of the induced intermediate space Z = im A + =im A −1 , in particular, for Γ = ℝ and Φ ε ζ[ C β (ℝ)] m × m which is of special interest in certain applications. As we know, this implies detailed results about the structure and the explicit asymptotic behaviour of solutions of boundary and transmission problems near singular points with a relation also to eigenvalue problems which result from the classical series expansion approach or from the Mellin symbol calculus (see [13]).