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On Reproducing Kernel Hilbert Spaces of Polynomials
Author(s) -
Li XianJin
Publication year - 1997
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.3211850110
Subject(s) - mathematics , reproducing kernel hilbert space , hardy space , hilbert space , pure mathematics , norm (philosophy) , hilbert manifold , factorization , orthogonal polynomials , discrete mathematics , algorithm , political science , law
Certain Hilbert spaces of polynomials, called Szegö spaces [11], are studied. A transformation, called Hilbert traneformation, is constructed for every polynomial associatted with a Szegö space. An orthogonal set is found in a Szegö space which determines the norm of the space. A matrix factorization theory is obtained for defining polynomials. Measures associated with a Szegö space are parametrized by functions which ue analytic and bounded by one in the unit disk. A fundmental factorization theorem relates Szegö spaces to weighted Hardy spaces.