Affine and quasi-affine frames for rational dilations
نویسندگان
چکیده
منابع مشابه
On Affine Frames with Transcendental Dilations
We answer a question of O. Christensen about affine systems in L2(R). Specifically, we show that if the dilation factor a > 1 is transcendental, then cancellations cannot occur between different scales, in the conditions for the affine system to form a frame. Such cancellations are known to occur when a is an integer.
متن کاملOversampling, Quasi Affine Frames and Wave Packets
In [11], three of the authors obtained a characterization of certain types of reproducing systems. In this work, we apply these results and methods to various affine–like, wave packets and Gabor systems to determine their frame properties. In particular, we study how oversampled systems inherit properties (like the frame bounds) of the original systems. Moreover, our approach allows us to study...
متن کاملCompactly Supported Tight Affine Frames with Integer Dilations and Maximum Vanishing Moments
When a Cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L = L(IR) with dilation integer factor M ≥ 2, the standard “matrix extension” approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The notio...
متن کاملCompactly Supported Tight Affine Frames with Integer Dilations and Maximum Vanishing Moments1) by
When a Cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L2 = L2(IR) with dilation integer factor M ≥ 2, the standard “matrix extension” approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The not...
متن کاملRational Self-affine Tiles
An integral self-affine tile is the solution of a set equation AT = ⋃d∈D(T +d), where A is an n× n integer matrix and D is a finite subset of Z. In the recent decades, these objects and the induced tilings have been studied systematically. We extend this theory to matrices A ∈ Qn×n. We define rational self-affine tiles as compact subsets of the open subring R ×∏pKp of the adèle ring AK , where ...
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: Transactions of the American Mathematical Society
سال: 2011
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-2010-05200-6