two-direction poly-scale refinement equations with nonnegative coefficients
نویسندگان
چکیده
in this paper, we study l1 -solutions of the following two-direction poly-scale refinement equationwe prove that the vector space of all l1 -solutions of the above equation is at most one-dimensional andconsists of compactly supported functions of constant sign. we also show that any- l1 solution of the aboveequation is either positive or negative on its support under a special assumption. with regard to the -solutions of the equation, some simple sufficient conditions for the existence of nontrivial -solutions andthe nonexistence of such solutions are given.
منابع مشابه
Two-direction Poly-scale Refinement Equations with Nonnegative Coefficients
We prove that the vector space of all 1 L -solutions of the above equation is at most one-dimensional and consists of compactly supported functions of constant sign. We also show that any1 L solution of the above equation is either positive or negative on its support under a special assumption. With regard to the solutions of the equation, some simple sufficient conditions for the existence of ...
متن کاملPointwise Two-scale Expansion for Parabolic Equations with Random Coefficients
We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension 3 and higher and for coefficients having a finite range of dependence, we prove a pointwise version of the two-scale expansion. A similar expansion is derived for elliptic equations in divergence form. The result is surprising, since it was not expected to be true...
متن کاملSubdivision Schemes and Refinement Equations with Nonnegative Masks
We consider the two-scale refinement equation f(x) = ∑N n=0 cnf(2x − n) with ∑ n c2n = ∑ n c2n+1 = 1 where c0, cN 6= 0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all cn ≥ 0. It has long been conjectured that under such an assumption the subdivision algorithm converge, as well as the cascade algorithm converge unifo...
متن کاملPolynomials with Nonnegative Coefficients
The authors verify the conjecture that a conjugate pair of zeros can be factored from a polynomial with nonnegative coefficients so that the resulting polynomial still has nonnegative coefficients. The conjecture was originally posed by A. Rigler, S. Trimble, and R. Varga arising out of their work on the Beauzamy-Enflo generalization of Jensen's inequality. The conjecture was also made independ...
متن کاملOn Nonnegative Cosine Polynomials with Nonnegative Integral Coefficients
We show that there exist Po > 0 ar>d P\, ■■■ , Pn nonnegative integers, such that 0 < p(x) = Po + Pi cosx + • ■ • + Pn cos Nx and po -C s1/3 for .s = J2'J=oPj < improving on a result of Odlyzko who showed the existence of such a polynomial p that satisfies Po < (.slogs)1/3 . Our result implies an improvement of the best known estimate for a problem of Erdos and Szekeres. As our method is noncon...
متن کاملOn a system of difference equations with period two coefficients
We show that the system of difference equations
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
iranian journal of science and technology (sciences)ISSN 1028-6276
دوره 34
شماره 4 2010
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023