A Moment Problem and Joint q-Isometry Tuples

Anand, Akash; Chavan, Sameer

doi:10.1007/s11785-015-0516-1

Cited by 13 publications

(25 citation statements)

References 21 publications

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“… 3). This combined with Lemma 5.2 yields that {w n+1 − µ({0})χ {1} (n + 1)} n 0 is completely monotone.…”

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confidence: 72%

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Dirichlet polynomials and a moment problem

Chavan¹,

Sahu²

2021

Preprint

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Consider a linear functional L defined on the space D[s] of Dirichlet polynomials with real coefficients and the set D+[s] of nonnegative elements in D[s]. An analogue of the Riesz-Haviland theorem in this context asks: What are all D+[s]-positive linear functionals L, which are moment functionals? Since the space D[s], when considered as a subspace of C([0, ∞), R), fails to be an adapted space in the sense of Choquet, the general form of Riesz-Haviland theorem is not applicable in this situation. In an attempt to answer the forgoing question, we arrive at the notion of a moment sequence, which we call the Hausdorff log-moment sequence. Apart from an analogue of the Riesz-Haviland theorem, we show that any Hausdorff log-moment sequence is a linear combination of {1, 0, . . . , } and {f (log(n)} n 1 for a completely monotone function f : [0, ∞) → [0, ∞). Moreover, such an f is uniquely determined by the sequence in question.

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“… 3). This combined with Lemma 5.2 yields that {w n+1 − µ({0})χ {1} (n + 1)} n 0 is completely monotone.…”

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confidence: 72%

“…By theorems of Fubini and Morera, it is easily seen that F k is holomorphic in H log(j) (cf. [3,Proposition 4.1]). Let L be a holomorphic branch of log defined on the right half plane H j and define…”

Section: Proof Of Theorem 32mentioning

confidence: 99%

Dirichlet polynomials and a moment problem

Chavan¹,

Sahu²

2021

Preprint

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“…The first part can be obtained along the lines of the proof of Corollary 3.5. The first equality in the second part may be deduced from (i) and [5,Corollary 3.8] while the second one is an immediate consequence of the fact that D z n z m w(|z|)dA(z) = δ mn (m, n ∈ N) for any continuous function w : [0, 1] → (0, ∞).…”

Section: )mentioning

confidence: 99%

Dirichlet Spaces Associated with Locally Finite Rooted Directed Trees

Chavan

Pradhan

Trivedi

2017

Integr. Equ. Oper. Theory

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Abstract. Let T = (V, E) be a leafless, locally finite rooted directed tree. We associate with T a one parameter family of Dirichlet spaces Hq (q 1), which turn out to be Hilbert spaces of vector-valued holomorphic functions defined on the unit disc D in the complex plane. These spaces can be realized as reproducing kernel Hilbert spaces associated with the positive definite kernelwhere V≺ denotes the set of branching vertices of T , nv denotes the depth of v ∈ V in T , and P eroot , Pv (v ∈ V≺) are certain orthogonal projections.Further, we discuss the question of unitary equivalence of operators M(1) z and M (2) z of multiplication by z on Dirichlet spaces Hq associated with directed trees T 1 and T 2 respectively.

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“…given in part (i) of Theorem 2.11. Thus, using Remark 2.4 of [2], one may obtain the representing measure for M z on H(K λ,µ + K λ ′ ,µ ) to be given by…”

Section: Remark 23mentioning

confidence: 99%

On the sum of two subnormal kernels

Ghara

Kumar

2019

Journal of Mathematical Analysis and Applications

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We show, by means of a class of examples, that if K1 and K2 are two positive definite kernels on the unit disc such that the multiplication by the coordinate function on the corresponding reproducing kernel Hilbert space is subnormal, then the multiplication operator on the Hilbert space determined by their sum K1 + K2 need not be subnormal. This settles a recent conjecture of Gregory T. Adams, Nathan S. Feldman and Paul J. McGuire in the negative. We also discuss some cases for which the answer is affirmative.

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A Moment Problem and Joint q-Isometry Tuples

Cited by 13 publications

References 21 publications

Dirichlet polynomials and a moment problem

Dirichlet polynomials and a moment problem

Dirichlet Spaces Associated with Locally Finite Rooted Directed Trees

On the sum of two subnormal kernels

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