Shannon multiresolution analysis on the Heisenberg group
نویسندگان
چکیده
منابع مشابه
Shannon Multiresolution Analysis on the Heisenberg Group *
We present a notion of frame multiresolution analysis on the Heisenberg group, abbreviated by FMRA, and study its properties. Using the irreducible representations of this group, we shall define a sinc-type function which is our starting point for obtaining the scaling function. Further, we shall give a concrete example of a wavelet FMRA on the Heisenberg group which is analogous to the Shannon...
متن کاملMultiresolution analysis on the symmetric group
There is no generally accepted way to define wavelets on permutations. We address this issue by introducing the notion of coset based multiresolution analysis (CMRA) on the symmetric group, find the corresponding wavelet functions, and describe a fast wavelet transform for sparse signals. We discuss potential applications in ranking, sparse approximation, and multi-object tracking.
متن کاملSupplement to “ Multiresolution analysis on the symmetric group ”
Representations. For the purposes of this paper a representation of G over C is a matrix-valued function ρ : G → Cdρ×dρ such that ρ(x)ρ(y) = ρ(xy) for any x, y ∈ G. We call dρ the order or the dimensionality of ρ. Note that ρ(e) = I for any representation. Two representations ρ1 and ρ2 of the same dimensionality d are said to be equivalent if for some invertible T ∈ Cd×d, ρ1(x) = Tρ2(x)T for an...
متن کاملRiesz Potential on the Heisenberg Group
The relation between Riesz potential and heat kernel on the Heisenberg group is studied. Moreover , the Hardy-Littlewood-Sobolev inequality is established.
متن کاملInverse Radon Transforms on the Heisenberg Group
In this article, we introduce a kind of unitary operator U associated with the involution on the Heisenberg group, invariant closed subspaces are identified with the characterization spaces of sub-Laplacian operators. In the sense of vector-valued functions, we study the theory of continuous wavelet transform. Also, we obtain a new inversion formula of Radon transform on the Heisenberg group Hn.
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 Mathematical Analysis and Applications
سال: 2008
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2008.07.035