In this paper, after reviewing the main points of Haar wavelet transform and chaotic trigonometric maps, we introduce a new perspective of Haar wavelet transform. The essential idea of the paper is given linearity properties of the scaling function of the Haar wavelet. With regard to applications of Haar wavelet transform in image processing, we introduce chaotic trigonometric Haar wavelet tran...

We study moments of characteristic polynomials truncated Haar distributed matrices from the three classical compact groups [Formula: see text], text] and text]. For finite matrix size we calculate in terms hypergeometric functions argument give explicit integral representations highlighting duality between moment as well orthogonal symplectic cases. Asymptotic expansions strong weak non-unitari...

Let {Xij}, i, j = . . . , be a double array of i.i.d. complex random variables with EX11 = 0,E|X11| 2 = 1 and E|X11| 4 <∞, and let An = 1 N T 1/2 n XnX ∗ nT 1/2 n , where T 1/2 n is the square root of a nonnegative definite matrix Tn and Xn is the n×N matrix of the upper-left corner of the double array. The matrix An can be considered as a sample covariance matrix of an i.i.d. sample from a pop...

For each irreducible module of the symmetric group SN there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to two Hermitian forms, one called the contravariant form and the other is with respect to a matrix-valued measure on the N -to...

Digital databases can be represented by matrices, where rows (say) correspond to numerical sensors readings, or features, and columns correspond to data points. Recent data analysis methods describe the local geometry of the data points using a weighted affinity graph, whose vertices correspond to data points. We consider two geometries, or graphs one on the rows and one on the columns, such th...

Suppose that G is a compact Abelian group. If A ⊂ G then how small can ‖χA‖A(G) be? In general there is no non-trivial lower bound. In [5] Green and Konyagin showed that if Ĝ has sparse small subgroup structure and A has density α with α(1−α) ≫ 1 then ‖χA‖A(G) does admit a non-trivial lower bound. To complement this [11] addressed the case where Ĝ has rich small subgroup structure and further c...

The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is...

Suppose that G is a compact Abelian group. If A ⊂ G then how small can ‖χA‖A(G) be? In general there is no non-trivial lower bound. In [3] Green and Konyagin show that if Ĝ has sparse small subgroup structure and A has density α with α(1 − α) ≫ 1 then ‖χA‖A(G) does admit a non-trivial lower bound. In this paper we address, by contrast, groups with duals having rich small subgroup structure, spe...

Typical l 1-recovery limit of sparse vectors represented by concatenations of random orthogonal matrices Abstract. We consider the problem of recovering an N-dimensional sparse vector x from its linear transformation y = Dx of M (< N) dimension. Minimizing the l 1-norm of x under the constraint y = Dx is a standard approach for the recovery problem, and earlier studies report that the critical ...

S. Banach pointed out that the graph of generic (in sense Baire category) element $\text{Homeo}([0,1])$ has length $2$. J. Mycielski asked if measure theoretic dual holds, i.e., all but Haar null many Christensen) elements have We answer this question in affirmative. call $f \in \text{Homeo}([0,1]^d)$ singular it takes a suitable set full to nullset, and strongly is almost everywhere differenti...