Discrete orthogonal polynomials and difference equations of several variables
نویسندگان
چکیده
منابع مشابه
Discrete Orthogonal Polynomials and Difference Equations of Several Variables
The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.
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The second order partial difference equation of two variables Du := A1,1(x)∆1∇1u+A1,2(x)∆1∇2u+ A2,1(x)∆2∇1u+ A2,2(x)∆2∇2u + B1(x)∆1u+ B2(x)∆2u = λu, is studied to determine when it has orthogonal polynomials as solutions. We derive conditions on D so that a weight function W exists for which WDu is self-adjoint and the difference equation has polynomial solutions which are orthogonal with respe...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2007
ISSN: 0001-8708
DOI: 10.1016/j.aim.2006.09.012