Dimensions of the boundaries of self-similar sets.
Diophantine classes, dimension and Denjoy maps
DiPerna-Majda measures and uniform integrability
The purpose of this note is to discuss the relationship among Rosenthal's modulus of uniform integrability, Young measures and DiPerna-Majda measures. In particular, we give an explicit characterization of this modulus and state a criterion of the uniform integrability in terms of these measures. Further, we show applications to Fatou's lemma.
Dirichlet forms on quotients of shift spaces
We define thin equivalence relations ∼ on shift spaces and derive Dirichlet forms on the quotient space in terms of the nearest neighbour averaging operator. We identify the associated Laplace operator. The conditions are applied to some non-self-similar extensions of the Sierpiński gasket.
Dirichlet series induced by the Riemann zeta-function
The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form for in . Among other things, using the Haar measure on for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.
Discrepancies of point sequences on the Sierpiński carpet
Discrete marginal problem for complex measures
Discrete self-similar multifractals with examples from algebraic number theory
Disintegration and perfectness of measure spaces.
Disintegration theory on a constant field of non-seperable Hilbert spaces.
Disjointness of the convolutionsfor Chacon's automorphism
The purpose of this paper is to show that if σ is the maximal spectral type of Chacon’s transformation, then for any d ≠ d’ we have . First, we establish the disjointness of convolutions of the maximal spectral type for the class of dynamical systems that satisfy a certain algebraic condition. Then we show that Chacon’s automorphism belongs to this class.
Diskrepanz und Distanz von Maßen bezüglich konvexer und Jordanscher Mengen.
Distance sets, ratio sets and certain transformations of sets of real numbers
Distortion inequality for the Frobenius-Perron operator and some of its consequences in ergodic theory of Markov maps in
Asymptotic properties of the sequences (a) and (b) , where is the Frobenius-Perron operator associated with a nonsingular Markov map defined on a σ-finite measure space, are studied for g ∈ G = f ∈ L¹: f ≥ 0 and ⃦f ⃦ = 1. An operator-theoretic analogue of Rényi’s Condition is introduced. It is proved that under some additional assumptions this condition implies the L¹-convergence of the sequences (a) and (b) to a unique g₀ ∈ G. The general result is applied to some smooth Markov maps in ....
Distribution measures and Hausdorff dimensions.
Distribution of digits in integers: fractal dimensions and zeta functions
Distribution Preserving Sequences of Maps and Almost Constant Sequences on Finite Sets.
Distributional and Operational Integral Homogeneity over Local Fields.
Dividing measures and narrow operators
We use a new technique of measures on Boolean algebras to investigate narrow operators on vector lattices. First we prove that, under mild assumptions, every finite rank operator is strictly narrow (before it was known that such operators are narrow). Then we show that every order continuous operator from an atomless vector lattice to a purely atomic one is order narrow. This explains in what sense the vector lattice structure of an atomless vector lattice given by an unconditional basis is far...
Division space axiomatics