A class of parametric transforms that are based on unified representation of transform matrices in the form of sparse matrix products is described. Different families of transforms are defined within the introduced class. All transforms of one family can be computed with fast algorithms similar in structure to each other. In particular, the family of Haar-like transforms consists of discrete or...

In this work we study a version of the general question of how well a Haar distributed orthogonal matrix can be approximated by a random gaussian matrix. Here, we consider a gaussian random matrix Yn of order n and apply to it the Gram-Schmidt orthonormalization procedure by columns to obtain a Haar distributed orthogonal matrix Un. If F m i denotes the vector formed by the first m-coordinates ...

K.-H. Grr ochenig and A. Haas asked whether for every expanding integer matrix A 2 M n (Z) there is a Haar-type orthonormal wavelet basis having dilation factor A and translation lattice Z n. They proved that this is the case when the dimension n = 1. This paper shows that this is also the case when the dimension n = 2.

Let U be a Haar distributed matrix in U(n) or O(n). We show that after centering the two-parameter process W (s, t) = ∑ i≤⌊ns⌋,j≤⌊nt⌋ |Uij | 2 converges in distribution to the bivariate tied-down Brownian bridge.

We realized an imaging Mueller matrix microscope for nanostructure characterization. For investigations on nanoform characterization via images, we measured and simulated images of specially designed nanostructures. As approach towards machine learning evaluation in ellipsometry, calculated Haar-like features the observed a higher sensitivity to subwavelength off-diagonal elements compared micr...

Evidence for deep connections between number theory and random matrix theory has been noticed since the Montgomery-Dyson encounter in 1972 : the function fields case was studied by Katz and Sarnak, and the moments of the Riemann zeta function along its critical axis were conjectured by Keating and Snaith, in connection with similar calculations for randommatrices on the unitary group. This thes...

In this paper, we derive Haar wavelet operational matrix of the fractional integration and use it to obtain eigenvalues of fractional Sturm-Liouville problem. The fractional derivative is described in the Caputo sense. The efficiency of the method is demo nstrated by examples MSC: 26A33

In this paper, we derive Haar wavelet operational matrix of the fractional integration and use it to obtain eigenvalues of fractional Sturm-Liouville problem. The fractional derivative is described in the Caputo sense. The efficiency of the method is demonstrated by examples MSC: 26A33

Given any fixed N×N positive semi-definite diagonal matrix G ≥ 0 we derive the explicit formula for the density of complex eigenvalues for random matrices A of the form A = U √ G where the random unitary matrices U are distributed on the group U(N) according to the Haar measure.