14 research outputs found
On Spectral Theory of Compatible Random Inflation Systems
No full textSpindeler T. On Spectral Theory of Compatible Random Inflation Systems. Bielefeld: Universität Bielefeld; 2018
A note on measures vanishing at infinity
No full textSpindeler T, Strungaru N. A note on measures vanishing at infinity. REVIEWS IN MATHEMATICAL PHYSICS. 2019;31(2): 1950007.In this paper, we review the basic properties of measures vanishing at infinity and prove a version of the Riemann-Lebesgue lemma for Fourier transformable measures
Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition
No full textSpindeler T, Strungaru N. Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition. Mathematische Nachrichten. 2024;297(2):25.In this paper, we study the class of tempered distributions whose Fourier transform is a translation bounded measure and show that each such distribution in Rd has order at most 2d. We show the existence of the generalized Eberlein decomposition within this class of distributions, and its compatibility with all previous Eberlein decompositions. The generalized Eberlein decomposition for Fourier transformable measures and properties of its components are discussed. Lastly, we take a closer look at the absolutely continuous spectrum of measures supported on Meyer sets
Pure Point Diffraction and Almost Periodicity
No full textLenz D, Spindeler T, Strungaru N. Pure Point Diffraction and Almost Periodicity. Israel Journal of Chemistry . 2024;64(10-11): e202300158.This article deals with pure point diffraction and its connection to various notions of almost periodicity. We explain why the Fibonacci chain does not fit into the classical concept of Bohr almost periodicity and how it fits into the classes of mean, Besicovitch and Weyl almost periodic point sets. We report on recent results which characterize pure point diffraction as mean almost periodicity of the underlying structure, and discuss how the complex amplitudes fit into this picture
The (reflected) Eberlein convolution of measures
No full textLenz D, Spindeler T, Strungaru N. The (reflected) Eberlein convolution of measures. Indagationes Mathematicae. 2024;35(5):959-988.In this paper, we study the properties of the Eberlein convolution of measures and introduce a reflected version of it. For functions we show that the reflected Eberlein convolution can be seen as a translation invariant function-valued inner product. We study its regularity properties and show its existence on suitable sets of functions. For translation bounded measures we show that the (reflected) Eberlein convolution always exists along subsequences of the given sequence, and is a weakly almost periodic and Fourier transformable measure. We prove that if one of the two measures is mean almost periodic, then the (reflected) Eberlein convolution is strongly almost periodic. Moreover, if one of the measures is norm almost periodic, so is the (reflected) Eberlein convolution. (c) 2023 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved
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Shifts of finite type and random substitutions
No full textGohlke P, Rust D, Spindeler T. Shifts of finite type and random substitutions. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. 2019;39(9):5085-5103.We prove that every topologically transitive shift of finite type in one dimension is topologically conjugate to a subshift arising from a primitive random substitution on a finite alphabet. As a result, we show that the set of values of topological entropy which can be attained by random substitution subshifts contains the logarithm of all Perron numbers and so is dense in the positive real numbers. We also provide an independent proof of this density statement using elementary methods
Dynamical systems arising from random substitutions
No full textRandom substitutions are a natural generalisation of their classical `deterministic' counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently replaced by a word from a finite set of possible words according to a probability distribution. We discuss the subshifts associated with such substitutions and explore the dynamical and ergodic properties of these systems in order to establish the groundwork for their systematic study. Among other results, we show under reasonable conditions that such systems are topologically transitive, have either empty or dense sets of periodic points, have dense sets of linearly repetitive elements, are rarely strictly ergodic, and have positive topological entropy
Abstract almost periodicity for group actions on uniform topological spaces
No full textWe present a unified theory for the almost periodicity of functions with
values in an arbitrary Banach space, measures and distributions via almost
periodic elements for the action of a locally compact abelian group on a
uniform topological space. We discuss the relation between Bohr and Bochner
type almost periodicity, and similar conditions, and how the equivalence among
such conditions relates to properties of the group action and the uniformity.
We complete the paper by demonstrating how various examples considered earlier
all fit in our framework
