In this paper we show how to compute the Λα norm , α ≥ 0, using the dyadic grid. This result is a consequence of the description of the Hardy spaces H(R ) in terms of dyadic and special atoms. Recently, several novel methods for computing the BMO norm of a function f in two dimensions were discussed in [9]. Given its importance, it is also of interest to explore the possibility of computing the...

At the 60 GHz band a massive amount of spectral space (5 GHz) has been allocated unlicensed worldwide for dense wireless local communications. OFDM has gained much popularity in the field of wireless communication because of its ability to transfer the data at higher rate, high bandwidth efficiency and robustness to multipath and delay.The BER performance of conventional FFT-OFDM system is comp...

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.

If G is a second countable locally compact Hausdorff groupoid with Haar system, we show that every representation induced from an irreducible representation of a stability group is irreducible.

Recently, we have been developing general multireso-lution signal decomposition schemes that unify traditional (linear) approaches and allow use of nonlinear ltering techniques in the decomposition. This paper summarizes our approach and provides several simple examples. Some of these examples are known in the literature (e.g., Haar pyramid and wavelet) and some of them are new (e.g., morpholog...

hybrid of rationalized haar functions are developed to approximate the solution of the differential equations. the properties of hybrid functions which are the combinations of block-pulse functions and rationalized haar functions are first presented. these properties together with the newton-cotes nodes are then utilized to reduce the differential equations to the solution of algebraic equation...

The Weyl criterion is shown in the terms of Price functions and Haar type functions. We define the so-called modified integrals of Price and Haar type functions and obtain the analogues of the criterion of Weyl, the inequalities of LeVeque and Erdös-Turan and the formula of Koksma in the terms of the modified integrals of Price and Haar type functions.

While optical character recognition is field where machine learning algorithms are easily applied, it might not always be cost effective to do so. While Viola and Jones explored Haar features in their face detection algorithm, selecting from the thousands of features is quite time consuming. This paper compares their feature set with a baseline of pixel learners as well as another set of Haar f...

For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M

In the paper we investigate the behavior of trajectory of rational p-adic dynamical system in complex p-adic filed Cp. It is studied Siegel disks and attractors of such dynamical systems. We show that Siegel disks may either coincide or disjoin for different fixed points of the dynamical system. Besides, we find the basin of the attractor of the system. It is proved that such kind of dynamical ...