Multi-Point Degenerate Interpolation Problem for Generalized Schur Functions: Description of All Solutions View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2011-09

AUTHORS

Vladimir Bolotnikov

ABSTRACT

We consider the Nevanlinna-Pick-Carathéodory-Fejér interpolation problem with finitely many interpolation conditions in the class Sgk of meromorphic functions f with ∥f∥l∞(t) ≤ 1 and with κ poles inside the unit disk D. The problem has infinitely many solutions if and only if κ is greater than or equal to the number of non-positive eigenvalues (counted with multiplicities) of the Pick matrix P constructed from interpolation data. For each such κ, we describe the solution set of the problem in terms of a family of linearfractional transformations with disjoint ranges. The parameters defining this family are free and independent. More... »

PAGES

143-160

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf03321794

DOI

http://dx.doi.org/10.1007/bf03321794

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1051221567


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