On Fourier frame of absolutely continuous measures

Absolutely Continuous Invariant Measures That Are Maximal

Let A be a certain irreducible 0-1 matrix and let t denote the family of piecewise linear Markov maps on [0,1] which are consistent with A. The main result of this paper characterizes those maps in t whose (unique) absolutely continuous invariant measure is maximal, and proves that for "most" of the maps that are consistent with A, the absolutely continuous invariant measure is not maximal.

An Approximation for the Fourier Transform of Absolutely Continuous Mappings

The Fourier Transform is an important mathematical tool in a wide variety of fields of science and engineering [1, p. XI]. In this paper, by the use of some integral identities and inequalities developed in [2](see also [3]), we point out some approximations of the Fourier transform in terms of the complex exponential mean, E (z, w) (see Section 2) and study the error of approximation for diffe...

On Absolutely Continuous Transformations

Convergence on Manifolds of Gibbs Measures Which Are Absolutely Continuous with Respect to Hausdorff Measures

We identify a sufficiant condition for a sequence of Gibbs measures Pλ with the density Zλe01, v ∈ Rn, defined on a state space of v′s, to converge weakly in a sense of measures to a Gibbs measure with a density Zλe −J0(v), where the dominating measure for the density is the Hausdorff measure with an appropriate dimension. The function J0 identifies an objective and J1 defines a constraint. The...

The Existence of Absolutely Continuous Local Martingale Measures

We investigate the existence of an absolutely continuous martingale measure. For continuous processes we show that the absence of arbitrage for general admissible integrands implies the existence of an absolutely continuous (not necessarily equivalent) local martingale measure. We also rephrase Radon-Nikodym theorems for predictable processes. 1.Introduction. In our paper Delbaen and Schacherma...