The Schur Transformation for Nevanlinna Functions: Operator Representations, Resolvent Matrices, and Orthogonal Polynomials View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2009

AUTHORS

D. Alpay , A. Dijksma , H. Langer

ABSTRACT

A Nevanlinna function is a function which is analytic in the open upper half-plane and has a non-negative imaginary paxt there. In this paper we study a fractional linear transformation for a Nevanlinna function n with a suitable asymptotic expansion at ∞, that is an analogue of the Schur transformation for contractive analytic functions in the unit disk. Applying the transformation p times we find a Nevanlinna function n p which is a fractional linear transformation of the given function n. The main results concern the effect of this transformation to the realizations of n and n p by which we mean their representations through resolvents of self-adjoint operators in Hilbert space. Our tools are block operator matrix representations, u-resolvent matrices, and reproducing kernel Hilbert spaces. More... »

PAGES

27-63

Book

TITLE

Modern Analysis and Applications

ISBN

978-3-7643-9918-4
978-3-7643-9919-1

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-7643-9919-1_4

DOI

http://dx.doi.org/10.1007/978-3-7643-9919-1_4

DIMENSIONS

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