Polynomial solutions to constant coefficient differential equations
نویسندگان
چکیده
منابع مشابه
Polynomial Solutions to Constant Coefficient Differential Equations
Let Dx, ... , Dr e C[d/dxx, ... , d/dxn) be constant coefficient differential operators with zero constant term. Let S = {fe C[xx,... , x„]\Dj(f) = 0 for all 1 < j < r) be the space of polynomial solutions to the system of simultaneous differential equations Dj(f) = 0. It is proved that S is a module over 3¡(V), the ring of differential operators on the affine scheme V with coordinate ring C[d/...
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Suppose p is a homogeneous polynomial over a field K. Let p(D) be the differential operator defined by replacing each occurrence of xj in p by xj , defined formally in case K is not a subset of C. (The classical example is p(x1 , ..., xn)= j xj , for which p(D) is the Laplacian { .) In this paper we solve the equation p(D) q=0 for homogeneous polynomials q over K, under the restriction that K b...
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1 We investigate the zeros of polynomial solutions to the differential-difference equation P n+1 (x) = A n (x)P ′ n (x) + B n (x)P n (x), n = 0, 1,. .. where A n and B n are polynomials of degree at most 2 and 1 respectively. We address the question of when the zeros are real and simple and whether the zeros of polynomials of adjacent degree are interlac-ing. Our result holds for general classe...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1992
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1992-1013339-6