An infinite dimensional umbral calculus

Finkelshtein D, Kondratiev Y, Lytvynov E, Oliveira MJ (2019)
JOURNAL OF FUNCTIONAL ANALYSIS 276(12): 3714-3766.

Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Zeitschriftenaufsatz | Veröffentlicht | Englisch
Autor
; ; ;
Abstract / Bemerkung
The aim of this paper is to develop foundations of umbral calculus on the space D' of distributions on R-d, which leads to a general theory of Sheffer polynomial sequences on D'. We define a sequence of monic polynomials on, a polynomial sequence of binomial type, and a Sheffer sequence. We present equivalent conditions for a sequence of monic polynomials on D' to be of binomial type or a Sheffer sequence, respectively. We also construct a lifting of a sequence of monic polynomials on R of binomial type to a polynomial sequence of binomial type on D', and a lifting of a Sheffer sequence on R to a Sheffer sequence on D'. Examples of lifted polynomial sequences include the falling and rising factorials on D', Abel, Hermite, Charlier, and Laguerre polynomials on D'. Some of these polynomials have already appeared in different branches of infinite dimensional (stochastic) analysis and played there a fundamental role. (C) 2019 Elsevier Inc. All rights reserved.
Erscheinungsjahr
Zeitschriftentitel
JOURNAL OF FUNCTIONAL ANALYSIS
Band
276
Ausgabe
12
Seite(n)
3714-3766
ISSN
eISSN
PUB-ID

Zitieren

Finkelshtein D, Kondratiev Y, Lytvynov E, Oliveira MJ. An infinite dimensional umbral calculus. JOURNAL OF FUNCTIONAL ANALYSIS. 2019;276(12):3714-3766.
Finkelshtein, D., Kondratiev, Y., Lytvynov, E., & Oliveira, M. J. (2019). An infinite dimensional umbral calculus. JOURNAL OF FUNCTIONAL ANALYSIS, 276(12), 3714-3766. doi:10.1016/j.jfa.2019.03.006
Finkelshtein, D., Kondratiev, Y., Lytvynov, E., and Oliveira, M. J. (2019). An infinite dimensional umbral calculus. JOURNAL OF FUNCTIONAL ANALYSIS 276, 3714-3766.
Finkelshtein, D., et al., 2019. An infinite dimensional umbral calculus. JOURNAL OF FUNCTIONAL ANALYSIS, 276(12), p 3714-3766.
D. Finkelshtein, et al., “An infinite dimensional umbral calculus”, JOURNAL OF FUNCTIONAL ANALYSIS, vol. 276, 2019, pp. 3714-3766.
Finkelshtein, D., Kondratiev, Y., Lytvynov, E., Oliveira, M.J.: An infinite dimensional umbral calculus. JOURNAL OF FUNCTIONAL ANALYSIS. 276, 3714-3766 (2019).
Finkelshtein, Dmitri, Kondratiev, Yuri, Lytvynov, Eugene, and Oliveira, Maria Joao. “An infinite dimensional umbral calculus”. JOURNAL OF FUNCTIONAL ANALYSIS 276.12 (2019): 3714-3766.