Linear independence of translates of a box spline
نویسندگان
چکیده
منابع مشابه
Linear Independence of Time-frequency Translates
Abstract. The refinement equation φ(t) = ∑N2 k=N1 ck φ(2t − k) plays a key role in wavelet theory and in subdivision schemes in approximation theory. Viewed as an expression of linear dependence among the time-scale translates |a|1/2φ(at − b) of φ ∈ L2(R), it is natural to ask if there exist similar dependencies among the time-frequency translates e2πibtf(t + a) of f ∈ L2(R). In other words, wh...
متن کاملLinear Independence of Time Frequency Translates for Special Configurations
We prove that for any 4 points in the plane that belong to 2 parallel lines, there is no linear dependence between the associated time-frequency translates of any nontrivial Schwartz function. If mild Diophantine properties are satisfied, we also prove linear independence in the category of L2(R) functions.
متن کاملLinear Independence of Time-frequency Translates in R
We establish the linear independence of time-frequency translates for functions f on R having one sided decay limx∈H, |x|→∞ |f(x)|ec|x| log |x| = 0 for all c > 0, which do not vanish on an affine half-space H ⊂ R.
متن کاملOn linear independence of T-spline blending functions
This paper shows that, for any given T-spline, the linear independence of its blending functions can be determined by computing the nullity of the T-spline-to-NURBS transform matrix. The paper analyzes the class of Tsplines for which no perpendicular T-node extensions intersect, and shows that the blending functions for any such T-spline are linearly independent.
متن کاملOn Linear Independence for Integer Translates of a Finite Number of Functions
We investigate linear independence of integer translates of a finite number of compactly supported functions in two cases. In the first case there are no restrictions on the coefficients that may occur in dependence relations. In the second case the coefficient sequences are restricted to be in some ` space (1 ≤ p ≤ ∞) and we are interested in bounding their `-norms in terms of the L-norm of th...
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 Approximation Theory
سال: 1984
ISSN: 0021-9045
DOI: 10.1016/0021-9045(84)90026-1