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Baxter algebras and the umbral calculus
, 2004
"... 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 λumbral calculi parame ..."
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Cited by 3 (3 self)
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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 λumbral calculi
Formal 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 ..."
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Cited by 2 (0 self)
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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
Umbral calculus: A model . . .
, 2008
"... We are working in the threeborderspoint between combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on grouplike structures). The profit from the “contraband” in all directions is investigated. ..."
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We are working in the threeborderspoint between combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on grouplike structures). The profit from the “contraband” in all directions is investigated.
An introduction to Umbral Calculus
, 1998
"... The aim of these lectures is to give an introduction to combinatorial aspects of Umbral Calculus. Seen in this light, Umbral Calculus is a theory of polynomials that count combinatorial objects. In the first two lectures we present the basics of Umbral Calculus as presented in the seminal papers Mul ..."
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Cited by 1 (0 self)
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The aim of these lectures is to give an introduction to combinatorial aspects of Umbral Calculus. Seen in this light, Umbral Calculus is a theory of polynomials that count combinatorial objects. In the first two lectures we present the basics of Umbral Calculus as presented in the seminal papers
Umbral presentations for polynomial sequences.
, 1999
"... Using random variables as motivation, this paper presents an exposition of formalisms developed in [RT1, RT2] for the classical umbral calculus. A variety of examples are presented, culminating in several descriptions of sequences of binomial type in terms of umbral polynomials. 1 ..."
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Cited by 7 (0 self)
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Using random variables as motivation, this paper presents an exposition of formalisms developed in [RT1, RT2] for the classical umbral calculus. A variety of examples are presented, culminating in several descriptions of sequences of binomial type in terms of umbral polynomials. 1
Umbral calculus in positive characteristic
 Adv. Appl. Math
"... Partially supported by CRDF under Grant UM12567OD03 An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in the space of continuous Fqlinear functions are constructed. Key ..."
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Cited by 4 (4 self)
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Partially supported by CRDF under Grant UM12567OD03 An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in the space of continuous Fqlinear functions are constructed. Key
Quantum mechanics and umbral calculus
, 805
"... In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schrödinger equation substituting the continuous derivatives by discrete ones and the spacetime continuous variables by well determined ope ..."
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operators that verify some Umbral Calculus conditions. In this way we assure that some properties of integrability and symmetries of the continuous equation are preserved and also the solutions of the continuous case can be recovered discretized in a simple way. The case of the Schrödinger equation with a
Maple Umbral Calculus Package
, 1995
"... Rota's Umbral Calculus uses sequences of Sheffer polynomials to count certain combinatorial objects. We have developed a Maple package that implements Rota's Umbral Calculus and some of its generalizations. A Mathematica version of this package is being developed in parallel. ..."
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Rota's Umbral Calculus uses sequences of Sheffer polynomials to count certain combinatorial objects. We have developed a Maple package that implements Rota's Umbral Calculus and some of its generalizations. A Mathematica version of this package is being developed in parallel.
Universal constructions in umbral calculus
 Mathematical Essays in Honor of GianCarlo Rota Birkhauser
, 1998
"... Modern umbral calculus is steadily approaching maturity, as applications develop in several areas of mathematics. To maximize this utility it is important to work in the most general (as opposed to the most abstract) ..."
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Cited by 2 (0 self)
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Modern umbral calculus is steadily approaching maturity, as applications develop in several areas of mathematics. To maximize this utility it is important to work in the most general (as opposed to the most abstract)
Results 1  10
of
2,718