منابع مشابه
On minimal cubature formulae for product weight functions 1
We derive in a simple way certain minimal cubature formulae, obtained by Morrow and Patterson [2], and Xu [4], using a different technique. We also obtain in explicit form new near minimal cubature formulae. Then, as a corollary, we get a compact expression for the bivariate Lagrange interpolation polynomials, based on the nodes of the cubature.
متن کاملMATRIX Ap WEIGHTS VIA MAXIMAL FUNCTIONS
Weighted Norm theory forms a basic component of the study of singular integrals. Here one attempts to characterize those measure spaces over which a broad class of singular integral operators remain bounded. For the case of singular integral operators on C-valued functions in Euclidean space, the answer is given by the Hunt-Muckenhoupt-Wheeden theorem [10]. It states that the necessary and suff...
متن کاملMATRIX Ap WEIGHTS VIA S-FUNCTIONS
The statement of the problem. In this paper we study weighted norm inequalities with matrix valued weights. Namely, let W be a d × d matrix weight, i.e. a L-function whose values are selfadjoint nonnegative d × d matrices. We suppose that the weight W is defined on the unit circle T = {z ∈ C : |z| = 1} or the real line R. Let L = L(C) be the space of all measurable vector functions on T whose C...
متن کاملCartesian Product of Functions
For simplicity we follow the rules: x, y, y1, y2, z, a will be arbitrary, f , g, h, h′, f1, f2 will denote functions, i will denote a natural number, X, Y , Z, V1, V2 will denote sets, P will denote a permutation of X, D, D1, D2, D3 will denote non-empty sets, d1 will denote an element of D1, d2 will denote an element of D2, and d3 will denote an element of D3. We now state a number of proposit...
متن کاملOrthogonal Polynomials for a Family of Product Weight Functions on the Spheres
Based on the theory of spherical harmonics for measures invariant under a finite reflection group developed by Dunkl recently, we study orthogonal polynomials with respect to the weight functions jx1jã1 Ð Ð Ð jxdjãd on the unit sphere Sd 1 in Rd. The results include explicit formulae for orthonormal polynomials, reproducing and Poisson kernel, as well as intertwining operator.
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: Journal of the Institute of Engineering
سال: 2016
ISSN: 1810-3383
DOI: 10.3126/jie.v11i1.14703