Umbral Calculus and Cancellative Semigroup Algebras
نویسندگان
چکیده
منابع مشابه
Umbral Calculus and Cancellative Semigroup Algebras∗
We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of cancellative semigroup, their convolution algebras, and tokens between them provides a common language for description of objects from these three fields.
متن کاملAlgebras and the Umbral Calculus ∗
We apply Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that include the classical umbral calculus in a family of λ-umbral calculi parameterized by λ in the base ring.
متن کاملBaxter Algebras and the Umbral Calculus
We apply Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that include the classical umbral calculus in a family of-umbral calculi parameterized by in the base ring.
متن کاملFormal Calculus and Umbral Calculus
We use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus. We begin by calculating the exponential generating function of the higher derivatives of a composite function, following a very short proof which naturally arose as a motivating computation related to a certain crucial “associativity” property of an im...
متن کاملComputer algebra and Umbral Calculus
Rota's Umbral Calculus uses sequences of Sheffer polynomials to count certain combinatorial objects. We review this theory and some of its generalizations in light of our computer implementation (Maple V.3). A Mathematica version of this package is being developed in parallel.
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ژورنال
عنوان ژورنال: Zeitschrift für Analysis und ihre Anwendungen
سال: 2000
ISSN: 0232-2064
DOI: 10.4171/zaa/953