An Operator Calculus Based on The Cauchy—Green Formula, and the Quasi Analyticity of the Classes D(h)

1972 ◽  
pp. 128-131
Author(s):  
E. M. Dyn’kin
Keyword(s):  
Green Formula ◽  
Operator Calculus

An operator calculus based on the Cauchy-Green formula

1975 ◽  
Vol 4 (4) ◽  
pp. 329-334 ◽  
Author(s):  
E. M. Dyn'kin
Keyword(s):  
Green Formula ◽  
Operator Calculus

scholarly journals Towards ψ-extension of Rota's finite operator calculus

2001 ◽  
Vol 48 (3) ◽  
pp. 305-342 ◽  
Author(s):  
A.K Kwaśniewski
Keyword(s):  
Operator Calculus

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.

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