منابع مشابه
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Consider two differential operators L1 = ∑ aid i and L2 = ∑ bjd j with coefficients in a differential field, say C(t) with d = ∂ ∂t for example. If the ai and bj are constants, the condition for the existence of a solution y of L1(y) = L2(y) = 0 is that the resultant in X of the polynomials (in C[X]) ∑ aiX i and ∑ bjX j is zero. A natural question is: how one could extend this for the case of n...
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Let k be a field of characteristic zero and let f ∈ k[x]. The m-th cyclic resultant of f is rm = Res(f, x − 1). We characterize polynomials having the same set of nonzero cyclic resultants. Generically, for a polynomial f of degree d, there are exactly 2 distinct degree d polynomials with the same set of cyclic resultants as f . However, in the generic monic case, degree d polynomials are uniqu...
متن کاملContinuous Symmetric Sobolev Inner Products
In this paper we consider the sequence of monic polynomials (Qn) orthogonal with respect to a symmetric Sobolev inner product. If Q2n(x) = Pn(x) and Q2n+1(x) = xRn(x), then we deduce the integral representation of the inner products such that (Pn) and (Rn) are, respectively, the corresponding sequences of monic orthogonal polynomials. In the semiclassical case, algebraic relations between such ...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2005
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870500261413