A moment problem for positive measures on the unit disc

Atzmon, Aharon

doi:10.2140/pjm.1975.59.317

Cited by 52 publications

(48 citation statements)

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“…We remark that the method of proof of Theorem 9.2 is adapted from Atzmon [6]. We also remark that an operator measure dλ is uniquely determined by (9.6) (Stone-Weierstrass); the same uniqueness remark applies in the context of Proposition 9.3 below.…”

Section: Olofsson Ieotmentioning

confidence: 88%

“…As an application of Theorem 9.1 we have the following variation of a moment problem considered by Atzmon [6]; see also [30,Theorem 3.7]. Proof.…”

Section: Operator Model Theory N-hypercontractionsmentioning

confidence: 98%

“…This more general modeling problem amounts to that of finding an isometry V = (V 1 , V 2 ) : H → H 1 ⊕ H 2 (0. 6) of H into H 1 ⊕ H 2 satisfying the intertwining relation…”

Section: Introductionmentioning

confidence: 99%

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An Operator-valued Berezin Transform and the Class of n-Hypercontractions

Olofsson¹

2007

Integr. equ. oper. theory

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We study an operator-valued Berezin transform corresponding to certain standard weighted Bergman spaces of square integrable analytic functions in the unit disc. The study of this operator-valued Berezin transform relates in a natural way to the study of the class of n-hypercontractions on Hilbert space introduced by Agler. To an n-hypercontraction T ∈ L(H) we associate a positive L(H)-valued operator measure dωn,T supported on the closed unit discD in a way that generalizes the above notion of operatorvalued Berezin transform. This construction of positive operator measures dωn,T gives a natural functional calculus for the class of n-hypercontractions. We revisit also the operator model theory for the class of n-hypercontractions. The new results here concern certain canonical features of the theory. The operator model theory for the class of n-hypercontractions gives information about the structure of the positive operator measures dωn,T . Mathematics Subject Classification (2000). Primary 47A20, 47A25; Secondary 47A45, 47B20.

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Section: Olofsson Ieotmentioning

confidence: 88%

“…As an application of Theorem 9.1 we have the following variation of a moment problem considered by Atzmon [6]; see also [30,Theorem 3.7]. Proof.…”

Section: Operator Model Theory N-hypercontractionsmentioning

confidence: 98%

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An Operator-valued Berezin Transform and the Class of n-Hypercontractions

Olofsson¹

2007

Integr. equ. oper. theory

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“…3 Notice that the -compactness of F is not essential in the proof of part (iii) of Proposition 1; indeed, the continuity of and the regularity of (cf. footnote 1 ) imply the inner regularity of which, in turn, yields…”

mentioning

confidence: 99%

Solving the truncated moment problem solves the full moment problem

Stochel¹

2001

Glasgow Math. J.

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“…. and the measure dρ(z) is situated on the whole C, on the half of C, on the rectangle, on the disc of radius R in C, and so on [1,2,8,9,16,29]; the consideration of a correspondence positive defined functions see also in [10,13,24]. For the beginning we consider (1.1) in the case m, n ∈ N 0 and dρ(z) defined on C. The second part of the article (Subsection 4) will be devoted to the interesting for mathematical physic infinite-dimensional generalization of such theory, where in the integral (1.1) we change C to a complex nuclear space.…”

Section: Introductionmentioning

confidence: 99%