Asymptotic spherical analysis on the Heisenberg group
نویسندگان
چکیده
منابع مشابه
Fine Asymptotic Geometry in the Heisenberg Group
For every finite generating set on the integer Heisenberg group H(Z), we know from a fundamental result of Pansu on nilpotent groups that the wordmetric has the large-scale structure of a Carnot-Carathéodory Finsler metric on the real Heisenberg group H(R). We study the properties of those limit metrics and obtain results about the geometry of word metrics that reflect the dependence on generat...
متن کاملCombinatorics and Spherical Functions on the Heisenberg Group
Let V be a finite dimensional Hermitian vector space and K be a compact Lie subgroup of U(V ) for which the representation of K on C[V ] is multiplicity free. One obtains a canonical basis {pα} for the space C[VR] of K-invariant polynomials on VR and also a basis {qα} via orthogonalization of the pα’s. The polynomial pα yields the homogeneous component of highest degree in qα. The coefficients ...
متن کاملShannon 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 کاملSpherical Functions for the Action of a Finite Unitary Group on a Finite Heisenberg Group
The action of the unitary group on the real Heisenberg group yields a Gelfand pair. The associated spherical functions are well known and have been computed independently by many authors. In this paper we develop a discrete counterpart to this story by replacing the real numbers by a finite field of odd characteristic. This produces a finite Gelfand pair whose spherical functions are computed e...
متن کاملtangent bishop spherical images of a biharmonic b-slant helix in the heisenberg group heis3
in this paper, biharmonic slant helices are studied according to bishop frame in the heisenberg group heis3. we give necessary and sufficient conditions for slant helices to be biharmonic. the biharmonic slant helices arecharacterized in terms of bishop frame in the heisenberg group heis3. we give some characterizations for tangent bishop spherical images of b-slant helix. additionally, we illu...
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: Colloquium Mathematicum
سال: 2010
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm118-1-13