Results 11 to 20 of about 3,259 (178)
, 1995 We are developing a Maple package of functions related to Rota's Umbral Calculus.
Bottreau, Anne +2 more
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Umbral calculus in positive characteristic
Advances in Applied Mathematics, 2004 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 $\mathbb F_q$-linear functions are constructed.
Anatoly N. Kochubei
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Journal of Mathematical Analysis and Applications, 2000 The author establishes some weaker characteristic conditions of the operator \(t_c\) and investigates invariant operators. It is shown that if an operator \(T\) can commute with one of the operators \(\sigma_p\) (\(p\neq 0\) and a root of unity), then \(T\) is an invariant operator.
Xiehua Sun
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Formal Calculus and Umbral Calculus [PDF]
The Electronic Journal of Combinatorics, 2010 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 ...
Thomas J. Robinson
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Umbral Calculus and Cancellative Semigroup Algebras
Zeitschrift für Analysis und ihre Anwendungen, 2000 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 semigroups, their convolution algebras, and tokens
Vladimir V. Kisil
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Baxter Algebras and the Umbral Calculus
Advances in Applied Mathematics, 2001 This papers aims to unite two mathematical areas championed by G.-C. Rota: umbral calculus and Baxter algebras. The umbral calculus refers to algebraic combinatorics of sequences of polynomials of binomial type and other related sequences. Rota showed how this is encapsulated by a certain `umbral algebra' consisting of linear functionals on these ...
Li Guo
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Journal of Mathematical Analysis and Applications, 1981 AbstractAn algebraic setting for the Roman-Rota umbral calculus is introduced. It is shown how many of the umbral calculus results follow simply by introducing a comultiplication map and requiring it to be an algebra map. The same approach is used to construct a q-umbral calculus.
Edwin Ihrig, Mourad E. H. Ismail
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Study of degenerate derangement polynomials by λ-umbral calculus
Demonstratio Mathematica, 2023 In the 1970s, Rota began to build completely rigid foundations for the theory of umbral calculus based on relatively modern ideas of linear functions and linear operators.
Yun Sang Jo, Park Jin-Woo
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Umbral calculus via integral transforms
Journal of Mathematical Analysis and Applications, 1988 AbstractWe present some standard results in the theory of polynomials of binomial type from a different point of view. This approach is related to a theory of representations of canonical transformations.
Henryk Gzyl
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