Operator Moment Problems

Abstract

ZE n (STIELTJES moment problem), if G = IRd (G = R; ). We call the moment problem onesided (two-sided), if I = I N: (I = Z d ) .Remark. We could have used also notations like "operator moment problem" (as in the headline) or "X-moment problem" and "X-moment sequence" instead of "moment problem" and "moment sequence", resp. But there is no danger of confusion and the notation is justified, since we obtain classical moment problems by considering X = C. tjX,, X , E .X, where X , = 0 resp. I = Z d . G Let 3'7 denote the vector space of all functions t H f e I for all but finitely m a n y j E I , defined on IRd resp. (R \ ( 0 ) ) d if Z = 18*

Multivariate Determinateness

“…The case d ≥ 3 is more complicated and will be treated afterwards. The following theorem is closely related to Theorem 22 in [15].…”

“…Pioneering results belong to A. Devinatz [12], G.I. Eskin [14], J. Friedrich [15] and others. In this section we develop some general results of this kind and offer new proofs, again relying essentially on self-adjointness theory.…”