A ug 2 00 9 SPECTRAL GAPS FOR SETS AND MEASURES
نویسنده
چکیده
If X is a closed subset of the real line, denote by GX the supremum of the size of the gap in the Fourier spectrum, taken over all non-trivial finite complex measures supported on X. In this paper we attempt to find GX in terms of metric properties of X.
منابع مشابه
ar X iv : 0 90 8 . 20 79 v 1 [ m at h . C V ] 1 4 A ug 2 00 9 SPECTRAL GAPS FOR SETS AND MEASURES
If X is a closed subset of the real line, denote by GX the supremum of the size of the gap in the Fourier spectrum, taken over all non-trivial finite complex measures supported on X. In this paper we attempt to find GX in terms of metric properties of X.
متن کاملar X iv : m at h / 04 08 15 1 v 1 [ m at h . C A ] 1 1 A ug 2 00 4
In this paper, we study a class of quasi-invariant measures on paths generated by discrete dynamical systems. Our main result characterizes the subfamily of these measures which admit a certain desintegration. This is a desintegration with respect to a random walk Markov process which is indexed by the starting point of the paths. Our applications include wavelet constructions on Julia sets of ...
متن کاملA ug 2 00 6 Convexity of limits of harmonic measures
It is shown that, given a point x ∈ Rd, d ≥ 2, and open sets U1, . . . , Uk in Rd containing x, any convex combination of the harmonic measures εc n x for x with respect to Un, 1 ≤ n ≤ k, is the limit of a sequence (ε c m x )m∈N of harmonic measures, where each Wm is an open subset of U1 ∪ · · · ∪Uk containing x. This answers a question raised in connection with Jensen measures. More generally,...
متن کامل2 1 A ug 2 00 4 HAUSDORFF DIMENSION AND CONFORMAL MEASURES OF FEIGENBAUM JULIA SETS
We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the " hairiness phenomenon " , there exist many Feigenbaum Julia sets J(f) whose Hausdorff dimension is strictly smaller than two. We also prove that for any Feigen-baum Julia set, the Poincaré critical exponent δcr is equal to the hyperbolic dimension HD hyp (J(f)). Moreover, if a...
متن کاملDecision making in medical investigations using new divergence measures for intuitionistic fuzzy sets
In recent times, intuitionistic fuzzy sets introduced by Atanassov has been one of the most powerful and flexible approaches for dealing with complex and uncertain situations of real world. In particular, the concept of divergence between intuitionistic fuzzy sets is important since it has applications in various areas such as image segmentation, decision making, medical diagnosis, pattern reco...
متن کامل