Multiplicative Renormalization and Generating Functions Ii

Asai, Nobuhiro; Kubo, Izumi; Kuo, Hui-Hsiung

doi:10.11650/twjm/1500407706

Cited by 35 publications

(27 citation statements)

References 5 publications

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“…A method, called multiplicative renormalization method, has been introduced in [3,4] to answer this question. This method starts with an analytic function h(x) at 0.…”

Section: Multiplicative Renormalization Methodsmentioning

confidence: 99%

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Applicability of multiplicative renormalization method for a certain function

Kubo¹,

Kuo²,

Namli³

2008

COSA

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“…A method, called multiplicative renormalization method, has been introduced in [3,4] to answer this question. This method starts with an analytic function h(x) at 0.…”

Section: Multiplicative Renormalization Methodsmentioning

confidence: 99%

“…The resulting P n (x)'s are the well-known classical orthogonal polynomials. For the derivation, see [3,4]. Conversely, we have the following…”

Section: Definition 12 a Probability Measure µ Is Called Mrm-applicmentioning

confidence: 99%

Applicability of multiplicative renormalization method for a certain function

Kubo¹,

Kuo²,

Namli³

2008

COSA

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“…It is known that µ is symmetric if and only if α n = 0, n ≥ 0. Another way to derive the family (P n ) n is the multiplicative renormalization method ( [3], [4], [5], [6]) that we shall recall here : a nice function (u, x) → ψ(u, x) is a generating function for the measure µ if ψ has the expansion…”

Section: One-parameter Measures Family and Orthogonal Polynomialsmentioning

confidence: 99%

Free Martingale Polynomials for Stationary Jacobi Processes

Демни¹

2008

Quantum Probability and Related Topics

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Abstract. We generalize a previous result concerning free martingale polynomials for the stationary free Jacobi process of parameters λ ∈]0.1], θ = 1/2. Hopelessly, apart from the case λ = 1, the polynomials we derive are no longer orthogonal with respect to the spectral measure. As a matter of fact, we use the multiplicative renormalization method to write down its corresponding orthogonal polynomials as well as the orthogonality measure associated with the martingale polynomials. We finally give a realization of the spectral measure of the free stationary Jacobi process by means of the corresponding one mode interacting Fock space.

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“…The numbers α n and w n are called Szegö-Jacobi parameters of µ. (see [2,3,4,19] for detailed development). The classical polynomials of Legendre, Chebyshev of the first kind, Chebyshev of the second kind and Gegenbauer are distinguished from their generating function, which involves the Fourier transform of their orthogonality measure.…”

mentioning

confidence: 99%

“…From the paper [3], we recall the following useful background. Apply the GramSchmidt orthogonalization process to the sequence 1,…”

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confidence: 99%