Constant coefficient differential operators with slowly spreading solutions
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/...
متن کاملHomogeneous Polynomial Solutions to Constant Coefficient PDE's
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...
متن کاملSlowly Oscillating Solutions for Differential Equations with Strictly Monotone Operator
The authors discuss necessary and sufficient conditions for the existence and uniqueness of slowly oscillating solutions for the differential equation u′ + F(u) = h(t) with strictly monotone operator. Particularly, the authors give necessary and sufficient conditions for the existence and uniqueness of slowly oscillating solutions for the differential equation u′ +∇Φ(u)= h(t), where∇Φ denotes t...
متن کاملRight inverses for linear, constant coefficient partial differential operators on distributions over open half spaces
Results of Hörmander on evolution operators together with a characterization of the present authors [Ann. Inst. Fourier, Grenoble 40, 619 – 655 (1990)] are used to prove the following: Let P 2 Cz1; . . . ; zn and denote by Pm its principal part. If P ÿ Pm is dominated by Pm then the following assertions for the partial differential operators P D and Pm D are equivalent for N 2 Snÿ1: (1) P D...
متن کاملA Vanishing Conjecture on Differential Operators with Constant Coefficients
In the recent progress [BE1], [Me] and [Z2], the wellknown JC (Jacobian conjecture) ([BCW], [E]) has been reduced to a VC (vanishing conjecture) on the Laplace operators and HN (Hessian nilpotent) polynomials (the polynomials whose Hessian matrix are nilpotent). In this paper, we first show the vanishing conjecture above, hence also the JC, is equivalent to a vanishing conjecture for all 2nd or...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 1979
ISSN: 0025-5831,1432-1807
DOI: 10.1007/bf01428800