Abstract. Gröchenig and Madych showed that a Haar-type wavelet basis of L2(Rn) can be constructed from the characteristic function χΩ of a compact set Ω if and only if Ω is an integral self-affine tile of Lebesgue measure one. In this paper we generalize their result to the multiwavelet settings. We give a complete characterization of Haar-type scaling function vectors χΩ(x) := [χΩ1 (x), . . . ...

We prove the existence of solutions to Monge’s transport problem between two compactly supported Borel probability measures in the Heisenberg group equipped with its Carnot-Carathéodory distance assuming that the initial measure is absolutely continuous with respect to the Haar measure of the group.

A locally compact quantum group is a pair (A,Φ) of a C-algebra A and a -homomorphism Φ from A to the multiplier algebra M(A ⊗ A) of the minimal C-tensor product A ⊗ A satisfying certain assumptions (see [K-V1] and [K-V2]). One of the assumptions is the existence of the Haar weights. These are densely defined, lower semi-continuous faithful KMS-weights satisfying the correct invariance propertie...

This paper aims to provide different approaches to text dependent speaker identification using DCT, Walsh and Haar transform along with use of spectrograms. Spectrograms obtained from speech samples are used as image database for the study undertaken. This image database is then subjected to various transforms. Using Euclidean distance as measure of similarity, most appropriate speaker match is...

Quantum groups have been studied intensively for the last two decades from various points of view. The underlying mathematical structure is that of an algebra with a coproduct. Compact quantum groups admit Haar measures. However, if we want to have a Haar measure also in the noncompact case, we are forced to work with algebras without identity, and the notion of a coproduct has to be adapted. T...

Let G be a real connected Lie group with polynomial volume growth, endowed with its Haar measure dx. Given a C positive function M on G, we give a sufficient condition for an L Poincaré inequality with respect to the measure M(x)dx to hold on G. We then establish a non-local Poincaré inequality on G with respect to M(x)dx.

Abstract We construct a class of non-reversible Metropolis kernels as multivariate extension the guided-walk kernel proposed by Gustafson ( Statist. Comput. 8 , 1998). The main idea our method is to introduce projection that maps state space totally ordered group. By using Haar measure, we novel Markov termed mixture kernel, which interest in its own right. This achieved inducing topological st...

Long term memory has frequently been observed in physical time series. Statistical theory for long term memory stochastic processes is radically different from the standard time series analysis, which assumes short term memory. The Allen variance is a particular measure of variability developed for long term memory processes. This variance can be interpreted as a Haar wavelet coefficient varian...