Truncated moment problems in the class of generalized Nevanlinna functions

Abstract

Truncated moment and related interpolation problems in the class of generalized Nevanlinna functions are investigated. General solvability criteria will be established and complete parametrizations of solutions are given. The framework used in the paper allows the treatment of even and odd order problems in a parallel manner. The main new results concern the case where the corresponding Hankel matrix of moments is degenerate. One of the new effects in the indefinite case is that the degenerate moment problem may have infinitely many solutions. However, with a careful application of an indefinite analogue of a step-by-step Schur algorithm a complete description of the set of solutions will be obtained.

On maximum mass measures in truncated matricial Hamburger moment problems and related interpolation problems

“…(11.10) and (C.2)] and the relation between the solutions of the form of matrix continued fractions and that of the linear fractional transformation established in [3, Section 4], we can obtain a description of the general solution τ to nondegenerate Problem (THM) 2n+1 . In the scalar case p = 1, the following result goes back to [7,Corollary 5.2].…”

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“…The following lemma is a direct corollary of Lemma . It collects some statements concerning asymptotic expansions of the reciprocal function from [, Lemma 2.1] and [, Lemma 2.13, Lemma A3]. Lemma Assume that a sequence satisfies the conditions with , let , and let b and the polynomial be defined by .…”

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