Bochner–Pearson-type characterization of the free Meixner class
نویسندگان
چکیده
منابع مشابه
Bochner-pearson-type Characterization of the Free Meixner Class
The operator Lμ : f 7→ ∫ f(x)−f(y) x−y dμ(y) is, for a compactly supported measure μ with an L density, a closed, densely defined operator on L(μ). We show that the operator Q = pLμ−qLμ has polynomial eigenfunctions if and only if μ is a free Meixner distribution. The only time Q has orthogonal polynomial eigenfunctions is if μ is a semicircular distribution. More generally, the only time the o...
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چکیده ندارد.
Free Meixner States
ABSTRACT. Free Meixner states are a class of functionals on non-commutative polynomials introduced in [Ans06]. They are characterized by a resolvent-type form for the generating function of their orthogonal polynomials, by a recursion relation for those polynomials, or by a second-order non-commutative differential equation satisfied by their free cumulant functional. In this paper, we construc...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2011
ISSN: 0196-8858
DOI: 10.1016/j.aam.2010.01.011