Closed Subspaces which are Attractors for Representations of the Cuntz Algebras

Jørgensen, Palle E. T.

doi:10.1007/978-3-0348-7881-4_11

Current Trends in Operator Theory and Its Applications 2004

DOI: 10.1007/978-3-0348-7881-4_11

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Closed Subspaces which are Attractors for Representations of the Cuntz Algebras

Palle E. T. Jørgensen

Abstract: We analyze the structure of co-invariant subspaces for representations of the Cuntz algebras ON for N = 2, 3, . . . , N < ∞, with special attention to the representations which are associated to orthonormal and tight-frame wavelets in L 2 (R) corresponding to scale number N .

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Cited by 2 publications

References 17 publications

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Operator-valued Gaussian processes and their covariance kernels

Jørgensen¹,

Tian²

2023

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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In this paper, we discuss a new framework for operator-valued Gaussian processes and their covariance kernels. Our emphasis is four-fold: (i) starting with a positive operator-valued measure (POVM) [Formula: see text], we present algorithms for constructing an associated centered, operator-valued, Gaussian process [Formula: see text] with [Formula: see text] as its covariance kernel; (ii) we present different classes of POVMs, and we examine the corresponding classes of operator-valued Gaussian processes [Formula: see text]; (iii) for the operator-valued Gaussian processes [Formula: see text] at hand, and the non-commutative framework, we present the corresponding Itô-integrals; and we (iv) outline features of the operator-valued setting which are different from the more familiar case of scalar-valued Gaussian processes.

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Operator-valued Gaussian processes and their covariance kernels

Jørgensen¹,

Tian²

2023

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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Dual-Shift Decomposition and Wavelets

Levan

Kubrusly

2014

Int. J. Wavelets Multiresolut Inf. Process.

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We introduce the notion of dual-shift decomposition of an arbitrary Hilbert space, which is given in terms of two unilateral shifts. After ensuring conditions for the existence of it, such a decomposition is then constructed for the concrete space ℒ2[0, 1], on which the two unilateral shifts are parts of the dilation-by-2 and the translation-by-1 on ℒ2(ℝ). Using multiresolution analysis (MRA) of wavelet theory it is shown the existence of a Haar-system-type orthonormal basis for ℒ2[0, 1], which is combined with the dual-shift decomposition to yield a refined decomposition for ℒ2[0, 1].

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Closed Subspaces which are Attractors for Representations of the Cuntz Algebras

Abstract: We analyze the structure of co-invariant subspaces for representations of the Cuntz algebras ON for N = 2, 3, . . . , N < ∞, with special attention to the representations which are associated to orthonormal and tight-frame wavelets in L 2 (R) corresponding to scale number N .

Cited by 2 publications

References 17 publications

Operator-valued Gaussian processes and their covariance kernels

Operator-valued Gaussian processes and their covariance kernels

Dual-Shift Decomposition and Wavelets

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