Functions in Lploc[0,∞) where 1 ≤ p ≤ ∞ can be considered as inputs to linear systems. However, hysteresis operators of Preisach type have only been defined on much smaller space of regulated (or Baire) functions. In this paper, we re-define Play operators so that they are well defined for real valued measurable functions. We show that this definition coincides with the older definition for con...

Let D be the open unit disk in the complex plane and ∂D the unit circle. Let dσ(w) be the normalized Lebesgue measure on the unit circle. We denote by L(C) (L for n=1) the space of C-valued Lebesgue square integrable functions on the unit circle. The Hardy space H(C) (H for n=1) is the closed linear span of C-valued analytic polynomials. We observe that L(C) = L ⊗ C and H(C) = H ⊗ C, where ⊗ de...

In this paper we investigate the behaviour of weighted maximal operators Marcinkiewicz type (C,?)-means ??,* p (f) := supn?P |??n(f)|/ n2/p?(2+?) in Hardy space Hp(G2) (0 < ? 1 and 2/(2 + ?)). It is showed that are bounded from dyadic to Lebesgue Lp(G2), a sense sharp. was also proved strong convergence theorem for (C, ?) means Walsh-Fourier series Hp(G2).

Any forward-in-time self-similar (localized-in-space) suitable weak solution to the 3D Navier-Stokes equations is shown to be infinitely smooth in both space and time variables. As an application, a proof of infinite space and time regularity of a class of a priori singular small self-similar solutions in the critical weak Lebesgue space L3,∞ is given.

The basic representation of the current group O(n, 1) X in the L 2 space over the generalized Lebesgue measure 1) ,

An algorithm is presented to compute good point sets and weights for discrete least squares polynomial approximation on a geometry Ω ⊂ R2. The criterion that is used is the minimisation of the Lebesgue constant of the corresponding least squares operator. In order to approximate the Lebesgue constant, we evaluate the Lebesgue function in a point set generated by a refinement method that is base...

For a measure-preserving transformation T which is a skew-product of a measure-preserving transformation S and a topological group endomorphism a, it is shown that the entropy h satisfies the following "addition theorem": h(T) = h(S) + h(o). Introduction. In a previous paper [4], conditions were given for a certain type of transformation of a G-space (G being a compact separable group) to have ...