RELATION BETWEEN FRACTAL MEASURES AND CANTOR MEASURES
نویسندگان
چکیده
منابع مشابه
Two measures on Cantor sets
We give an example of Cantor-type set for which its equilibrium measure and the corresponding Hausdorff measure are mutually absolutely continuous. Also we show that these two measures are regular in the Stahl–Totik sense. c ⃝ 2014 Elsevier Inc. All rights reserved. MSC: 30C85; 31A15; 28A78; 28A80
متن کاملGood Measures on Cantor Space
While there is, up to homeomorphism, only one Cantor space, i.e. one zero-dimensional, perfect, compact, nonempty metric space, there are many measures on Cantor space which are not topologically equivalent. The clopen values set for a full, nonatomic measure μ is the countable dense subset {μ(U) : U is clopen} of the unit interval. It is a topological invariant for the measure. For the class o...
متن کاملScattering on fractal measures
Abstract. We study the one-dimensional potential-scattering problem when the potential is a Radon measure with compact support. We show that the usual reflection and transmission amplitude r(p) and t (p) of an incoming wave eipx are well defined. We also show that the scattering problem on fractal potentials can be obtained as a limit case of scattering on smooth potentials. We then explain how...
متن کاملModular Fractal Measures
A notable example of a discontinuous-everywhere function that is not traditionally integrable, yet, when properly defined, can be integrated, is derivative of the Minkowski Question Mark function. Some subject matter overlaps that of [6]. This paper includes numerical results for the Fourier transform of the measure, its Mellin transform, and Poisson kernel. This document is a research diary no...
متن کاملLattice Models and Fractal Measures
XXX OBSOLETE XXX HALF-BAKED XXX The ideas described herein are confusingly presented, and are half-baked, incomplete, incoherent. Essentially all the ideas herein are presented more sensibly, more coherently in other papers on this website. Much of what was originally in this paper has been edited out, and moved to another paper, which presents the ideas in a much clearer fashion: see [9]. XXX ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2007
ISSN: 1225-1763
DOI: 10.4134/ckms.2007.22.2.241