On the moment problem in the bounded case

Torrano, Emilio; Guadalupe, Rafael

doi:10.1016/0377-0427(93)90159-9

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Hessenberg Matrix Associated With a Sum Of Measures1

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“…because the support of every µ i is compact. Second, remark that every matrix defines a subnormal operator in ℓ 2 [1,21,23]. These two properties allow us to extend Mantica's spectral techniques [17] to the complex plane.…”

Section: Hessenberg Matrix Associated With a Sum Of Measuresmentioning

confidence: 97%

Computing the Hessenberg matrix associated with a self-similar measure

Escribano

Giraldo

Sastre

et al. 2011

Journal of Approximation Theory

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We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures.We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures.Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix.

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Section: Hessenberg Matrix Associated With a Sum Of Measuresmentioning

confidence: 97%