Gorbachuk
Myroslav
Gohberg
Israel
true
2009
chapter
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.
http://link.springer.com/10.1007/978-3-7643-9919-1_4
en
27-63
2009-01-01
The Schur Transformation for Nevanlinna Functions: Operator Representations, Resolvent Matrices, and Orthogonal Polynomials
chapters
https://scigraph.springernature.com/explorer/license/
2019-04-15T13:31
f2ad6f5269fb5635d53217ee794d4b2bd13bfa413ccf3a21523fbe4f2be2ac3d
readcube_id
Langer
H.
Kochubei
Anatoly
Mathematical Sciences
Gennadiy
Popov
dimensions_id
pub.1050943660
Gorbachuk
Valentyna
Adamyan
Vadim M.
Pure Mathematics
978-3-7643-9919-1
Modern Analysis and Applications
978-3-7643-9918-4
D.
Alpay
Berezansky
Yurij
University of Groningen
Department of Mathematics, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands
A.
Dijksma
TU Wien
Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria
doi
10.1007/978-3-7643-9919-1_4
Basel
Birkhäuser Basel
Springer Nature - SN SciGraph project
Langer
Heinz
Ben-Gurion University of the Negev
Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel