For mixing Zd-actions generated by commuting automorphisms of a compact abelian group, we investigate the directional uniformity of the rate of periodic point distribution and mixing. When each of these automorphisms has finite entropy, it is shown that directional mixing and directional convergence of the uniform measure supported on periodic points to Haar measure occurs at a uniform rate ind...

We provide a new proof of a Frĕıman-type theorem. Specifically, suppose that G is a locally compact abelian group with a Haar measure μG. The δ-ball Bδ of a translation invariant metric is called d-dimensional if μG(B2δ′ ) 6 2 dμG(Bδ′ ) for all δ ′ ∈ (0, δ]. We show that if A is a compact neighborhood with μG(nA) 6 n μG(A) for all n > d log d, then A is contained in a O(d log d)-dimensional bal...

In this article, we present a general technique for analyzing the concentration of Haar measures on compact groups using the properties of certain kinds of random walks. As an application, we obtain a new kind of measure concentration for random unitary matrices, which allows us to directly establish the concentration of the empirical distribution of eigenvalues of a class of random matrices. T...

Wavelet transform (WT) is an important tool to analyze the time-frequency structure of a signal. The WT relies on prototype signal that called mother wavelet. However, there no single universal wavelet fits all signals. Thus, selection function might be challenging represent achieve optimum performance. There are some studies determine optimal for other biomedical signals; however, exists evalu...

Let M be a unitary matrix with eigenvalues t j , and let f be a function on the unit circle. Deene X f (M) = P f(t j). We derive exact and asymptotic for-mulae for the covariance of X f and X g with respect to the measures j(M)j 2 dM where dM is Haar measure and an irreducible character. The asymptotic results include an analysis of the Fej er kernel which may be of independent interest.

Steve S. C. Ou,* K. N. Liou, X. J. Wang, D. Hagan, A. Dybdahl, M. Mussetto, L. D. Carey, J. Niu, J. A. Kankiewicz, S. Kidder, and T. H. Vonder Haar Department of Atmospheric Sciences, University of California, Los Angeles, California, USA Northrop Grumman Space Technology, Redondo Beach, California, USA Department of Atmospheric Sciences, Texas A&M University, College Station, Texas, USA Cooper...

In this section, we give a brief review of the measure theory which will be used in later sections. We use [R, Chapters 1 and 2] as our main resource. A σ-algebra on a set X is a collectionM of subsets of X such that ∅ ∈M, if S ∈M, then X \ S ∈ M, and if a countable collection S1, S2, . . . ∈ M, then ∪i=1Si ∈ M. That is, M is closed under complements and countable unions, and contains the empty...

The theme of the work presented here is performance comparison of gradient mask texture based image retrieval techniques using global and local hybrid wavelet transforms generated from the combination of Walsh, Haar and Kekre transforms. Ternary image maps of Prewitt/Robert/Sobel filtered images are compared with '64-pattern' texture set generated using local and global hybrid wavelet...

In certain imaging applications, the captured images are corrupted by Poisson noise. For such images, Poisson unbiased risk estimate (PURE) has been proposed as an unbiased estimator of the mean square error between the original and estimated images. By minimizing PURE, noise can be reduced. PURE was originally defined in the Haar wavelet domain. Since the wavelet functions are isotropic in eve...