The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 38 Next

Displaying 741 – 760 of 2107

Showing per page

Gradual doubling property of Hutchinson orbits

Hugo Aimar, Marilina Carena, Bibiana Iaffei (2015)

Czechoslovak Mathematical Journal

The classical self-similar fractals can be obtained as fixed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, both have the doubling property. We prove that the elements of Hutchinson orbits possess the doubling...

Group-valued measures on coarse-grained quantum logics

Anna de Simone, Pavel Pták (2007)

Czechoslovak Mathematical Journal

In it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later () this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained...

Happy fractals and some aspects of analysis on metric spaces.

Stephen Semmes (2003)

Publicacions Matemàtiques

There has been a lot of interest and activity along the general lines of analysis on metric spaces recently, as in [2], [3], [26], [40], [41], [46], [48], [49], [51], [82], [83], [89], for instance. Of course this is closely related to and involves ideas concerning spaces of homogeneous type, as in [18], [19], [66], [67], [92], as well as sub-Riemannian spaces, e.g., [8], [9], [34], [47], [52], [53], [54], [55], [68], [70], [72], [73], [84], [86], [88]. In the present survey we try to give an introduction...

Harmonic analysis and the geometry of subsets of Rn.

Guy David, Stephen Semmes (1991)

Publicacions Matemàtiques

This subject has several natural points of view, but we shall start with the one that corresponds to the following question: Is there something like Littlewood-Paley theory which is useful for analyzing the geometry of subsets of Rn, in much the same way that traditional Littlewood-Paley theory is good for analyzing functions and operators?

Harmonic measures versus quasiconformal measures for hyperbolic groups

Sébastien Blachère, Peter Haïssinsky, Pierre Mathieu (2011)

Annales scientifiques de l'École Normale Supérieure

We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.

Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval II

Franz Hofbauer (1993)

Studia Mathematica

We construct examples of expanding piecewise monotonic maps on the interval which have a closed topologically transitive invariant subset A with Darboux property, Hausdorff dimension d ∈ (0,1) and zero d-dimensional Hausdorff measure. This shows that the results about Hausdorff and conformal measures proved in the first part of this paper are in some sense best possible.

Hausdorff and Fourier dimension

Thomas William Körner (2011)

Studia Mathematica

There is no constraint on the relation between the Fourier and Hausdorff dimension of a set beyond the condition that the Fourier dimension must not exceed the Hausdorff dimension.

Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations

Franz Hofbauer (2009)

Commentationes Mathematicae Universitatis Carolinae

We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation. We give a formula of the dimensions of such measures in terms of entropy and Lyapunov exponents. This is done for two choices of the weights using the recurrence...

Hausdorff and packing measure for thick solenoids

Michał Rams (2004)

Studia Mathematica

For a linear solenoid with two different contraction coefficients and box dimension greater than 2, we give precise formulas for the Hausdorff and packing dimensions. We prove that the packing measure is infinite and give a condition necessary and sufficient for the Hausdorff measure to be positive, finite and equivalent to the SBR measure. We also give analogous results, generalizing [P], for affine IFS in ℝ².

Currently displaying 741 – 760 of 2107