scholarly journals Homogeneous Polynomial Solutions to Constant Coefficient PDE's

1996 ◽  
Vol 117 (2) ◽  
pp. 179-192 ◽  
Author(s):  
Bruce Reznick
Keyword(s):  
Constant Coefficient ◽  
Homogeneous Polynomial ◽  
Polynomial Solutions

scholarly journals JACK POLYNOMIALS, GENERALIZED BINOMIAL COEFFICIENTS AND POLYNOMIAL SOLUTIONS OF THE GENERALIZED LAPLACE'S EQUATION

1998 ◽  
Vol 13 (09) ◽  
pp. 715-725 ◽  
Author(s):  
S. CHATURVEDI
Keyword(s):  
Homogeneous Polynomial ◽  
Binomial Coefficients ◽  
Jack Polynomials ◽  
Laplace’S Equation ◽  
Linear Combinations ◽  
Laplace's Equation ◽  
Polynomial Solutions ◽  
Sutherland Model ◽  
Generalized Binomial Coefficients

We discuss the symmetric homogeneous polynomial solutions of the generalized Laplace's equation which arises in the context of the Calogero–Sutherland model on a line. The solutions are expressed as linear combinations of Jack polynomials and the constraints on the coefficients of expansion are derived. These constraints involve generalized binomial coefficients defined through Jack polynomials. Generalized binomial coefficients for partitions of k up to k=6 are tabulated.

Polynomial solutions to linear PDEs with constant coefficients

2019 ◽  
Vol 26 (2) ◽  
pp. 287-293
Author(s):  
Vakhtang Lomadze
Keyword(s):  
Constant Coefficient ◽  
Polynomial Solutions ◽  
Constant Coefficients ◽  
Linear Pdes

Abstract In this note we are concerned with the question: When are the polynomial solutions to a system of linear constant coefficient PDEs dense in the set of all its solutions?

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