In this paper we consider the truncated Stieltjes matrix moment problem when the so-called information matrices are degenerate and describe the set of all solutions in terms of the linear fractional transformation using the fundamental matrix inequality method.
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Vladimir Bolotnikov, Degenerate Stieltjes Moment Problem and Associated -Inner Polynomials. Z. Anal. Anwend. 14 (1995), no. 3, pp. 441–468DOI 10.4171/ZAA/633