scholarly journals A Lipschitz estimate for Berezin’s operator calculus

2004 ◽  
Vol 133 (1) ◽  
pp. 127-131 ◽  
Author(s):  
L. A. Coburn
Keyword(s):  
Operator Calculus ◽  
Lipschitz Estimate

scholarly journals Obtaining Easily Sums of Powers on Arithmetic Progressions and Properties of Bernoulli Polynomials by Operator Calculus

2017 ◽  
Vol 9 (5) ◽  
pp. 73
Author(s):  
Do Tan Si
Keyword(s):  
Differential Operator ◽  
Generating Function ◽  
Arithmetic Progression ◽  
Bernoulli Polynomials ◽  
Bernoulli Numbers ◽  
Arithmetic Progressions ◽  
Operator Calculus ◽  
Sums Of Powers ◽  
The Way

We show that a sum of powers on an arithmetic progression is the transform of a monomial by a differential operator and that its generating function is simply related to that of the Bernoulli polynomials from which consequently it may be calculated. Besides, we show that it is obtainable also from the sums of powers of integers, i.e. from the Bernoulli numbers which in turn may be calculated by a simple algorithm.By the way, for didactic purpose, operator calculus is utilized for proving in a concise manner the main properties of the Bernoulli polynomials. 

Recent Progress in Implementing the Tensor Operator Calculus *,**

1989 ◽  
pp. 15-32
Author(s):  
L. C. Biedenharn ◽  
R. Le Blanc ◽  
J. D. Louck
Keyword(s):  
Recent Progress ◽  
Tensor Operator ◽  
Operator Calculus

scholarly journals Operator calculus

1978 ◽  
Vol 78 (1) ◽  
pp. 95-116 ◽  
Author(s):  
Philip Feinsilver
Keyword(s):  
Operator Calculus

Operator calculus and Appell systems

1996 ◽  
pp. 17-27
Author(s):  
Philip Feinsilver ◽  
René Schott
Keyword(s):  
Operator Calculus

scholarly journals On polynomials of Sheffer type arising from a Cauchy problem

2003 ◽  
Vol 2003 (33) ◽  
pp. 2119-2137
Author(s):  
D. G. Meredith
Keyword(s):  
Cauchy Problem ◽  
Heat Conduction ◽  
Parabolic Equations ◽  
Analytic Solution ◽  
Heat Conduction Problem ◽  
Laguerre Polynomials ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Operator Calculus ◽  
Classical Polynomials

A new sequence of eigenfunctions is developed and studied in depth. These theta polynomials are derived from a recent analytic solution of the canonical Cauchy problem for parabolic equations, namely, the inverse heat conduction problem. By appealing to the methods of the operator calculus, it is possible to categorize the new functions as polynomials of binomial and Sheffer types. The connection of the new set with the classical polynomials of Laguerre is carefully examined. Some integral relations involving the Laguerre polynomials and the theta polynomials are presented along with a number of binomial identities. The inverse heat conduction problem is revisited and an analytic solution depending on the generalized theta polynomials is presented.

An Operator Calculus for the Askey-Wilson Operator

2001 ◽  
Vol 5 (3-4) ◽  
pp. 347-362 ◽  
Author(s):  
Mourad E.H. Ismail
Keyword(s):  
Operator Calculus ◽  
Wilson Operator

On fluctuation problems in the theory of queues

1976 ◽  
Vol 8 (03) ◽  
pp. 548-583 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Generating Functions ◽  
Finite Differences ◽  
Historical Development ◽  
Banach Algebras ◽  
Point Of View ◽  
Mathematical Methods ◽  
Operator Calculus ◽  
Complex Functions

This paper gives a survey of the historical development of the solutions of various fluctuation problems in the theory of queues from the point of view of the mathematical methods used. These methods include Markov chains, Markov processes, integral equations, complex functions, generating functions, Laplace transforms, factorization of functions, operator calculus, Banach algebras and some particular methods, such as calculus of finite differences and combinatorics. In addition, the paper contains several recent results of the author for semi-Markov queuing processes.

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