Free martingale polynomials

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dc.creatorAnshelevich, Michael
dc.date2001-12-19
dc.date.accessioned2026-07-07T04:45:20Z
dc.date.available2026-07-07T04:45:20Z
dc.descriptionIn this paper we investigate the properties of the free Sheffer systems, which are certain families of martingale polynomials with respect to the free Levy processes. First, we classify such families that consist of orthogonal polynomials; these are the free analogs of the Meixner systems. Next, we show that the fluctuations around free convolution semigroups have as principal directions the polynomials whose derivatives are martingale polynomials. Finally, we indicate how Rota's finite operator calculus can be modified for the free context.
dc.descriptionAMS-LaTeX with Times fonts; 25 pages
dc.identifierhttps://arxiv.org/abs/math/0112194
dc.identifierhttp://arxiv.org/abs/math/0112194
dc.identifierJ. Funct. Anal. 201 (2003), 228-261
dc.identifierdoi:10.1016/S0022-1236(03)00061-2
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62919
dc.subjectCombinatorics
dc.subjectClassical Analysis and ODEs
dc.subjectOperator Algebras
dc.subjectProbability
dc.subject46L54; 05A40
dc.titleFree martingale polynomials
dc.typetext

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