A Basis for Polynomial Solutions to Systems of Linear Constant Coefficient PDE's

✍ Scribed by Paul S. Pedersen

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 261 KB
• Volume: 117
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1996.0005

✦ Synopsis

Let K represent either the real or the complex numbers. Let P k , k=1, 2, ..., r be constant coefficient (with coefficients from K) polynomials in n variables and let

r] be the set of all polynomial solutions (of degree M) to this system of partial differential equations. We solve the problem of finding an easily computed basis for the vector space N M . To do this we use a certain associative, and commutative algebra (defined over K), namely K[ ;]=K[; 1 , ; 2 , ..., ; n ] where [P k (;)=0 | k=1, ..., r] and

We show how the expression M j=0 (x 1 ; 1 + } } } +x n ; n ) j Âj! can be used to find an easily computed basis for N M .