1986
DOI: 10.1017/s0027763000022716
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Mixed periodic Jacobi continued fractions

Abstract: Let b0 be a positive real number andbe a Jacobi matrix. We can associate with them a Jacobi continued fraction, which will be abbreviated to a J fraction from the next section, as followswhere An(z)/Bn(z) is the n-th Padé approximant of φ(z).

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Cited by 8 publications
(10 citation statements)
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“…and it is understood that if ω m = 0 for some m, then the fraction terminates and, for convenience, we set ω n = α n = 0 for all n > m. In examples, we will mainly characterize measures by giving their Jacobi sequences and refer the reader to [13] for details and explicit measures. Let us also introduce the finite approximations of continued fractions which will be used in computations.…”
Section: )mentioning
confidence: 99%
See 1 more Smart Citation
“…and it is understood that if ω m = 0 for some m, then the fraction terminates and, for convenience, we set ω n = α n = 0 for all n > m. In examples, we will mainly characterize measures by giving their Jacobi sequences and refer the reader to [13] for details and explicit measures. Let us also introduce the finite approximations of continued fractions which will be used in computations.…”
Section: )mentioning
confidence: 99%
“…where P (z) = (z − 2α) 2 , A 2 = 2ω 2 , Λ 1 (z) = 3z − 2α and Γ 1 (z) = z 2 − zα + ω 2 , using the notation of [13,Theorem 3.4] (with N = 1, M = 1). Thus μ --μ is the measure with the absolutely continuous part given by the density…”
Section: Remark 92mentioning
confidence: 99%
“…The analytical study of infinite tridiagonal matrices (infinite Jacobi matrices, regarded as operators acting in ℓ 2 , the space of the square summable sequences of complex numbers) was considered before by several authors. For instance, in [8,9,11] in connection with the Theory of Toda Lattices, as well as in [14,18,19,23,25,26], where the spectrum of the corresponding Jacobi operators was studied. We also point out that a matrix theoretic approach to the problem concerning the study of the spectral properties of k−Toeplitz matrices has been presented in works by S. Serra Capizzano and D. Fasino [12,24].…”
Section: Introductionmentioning
confidence: 99%
“…Furthermore, the computation of the spectral measure n 0 0 (dX) also becomes an easier task. Compare with [71]; see also [73,74].…”
Section: • I \ -D U Z ••••mentioning
confidence: 99%