Hausdorff dimensions of level sets related to moving digit means
نویسندگان
چکیده
منابع مشابه
Adaptive Hausdorff Estimation of Density Level Sets
Hausdorff accurate estimation of density level sets is relevant in applications where a spatially uniform mode of convergence is desired to ensure that the estimated set is close to the target set at all points. The minimax optimal rate of error convergence for the Hausdorff metric is known to be (n/ logn) for level sets with Lipschitz boundaries, where the parameter α characterizes the regular...
متن کاملHausdorff Dimensions of Escaping Sets of Transcendental Entire Functions
Let f and g be transcendental entire functions, each with a bounded set of singular values, and suppose that g ◦ φ = ψ ◦ f , where φ, ψ : C → C are affine. We show that the escaping sets of f and g have the same Hausdorff dimension. Using a result of the second author, we deduce that there exists a family of transcendental entire functions for which the escaping set has Hausdorff dimension equa...
متن کاملAn Inequality for Hausdorff Means
We show that skyscrapers are possible even in cities like Meanie– apolis. This lofty assertion leads to a new class of elementary inequalities, the simplest example being v u u t 1 m m X
متن کاملTernary Basic Digit Sets
A radix representation of a real number, for an integral base B ≥ 2 and digit set D, is a string of digits (an...a1a0...)B = ∑∞ i=−n a−iB , with ak ∈ D. It is commonly known that using a digit set of the form {0, 1, ..., B−1}, any positive real number has a B-ary radix representation. This is simply the standardB-ary representation of a number. Alternative digit representations have been of pra...
متن کاملAdmissible digit sets
We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a finite number of Möbius transformations. We regard certain sets of Möbius transformations as a generalized notion of digits and introduce sufficient conditions that such a “digit set” yields an admissible representation of [0,+∞]. Furthermore we establish the productivity ...
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: Journal of Mathematical Analysis and Applications
سال: 2020
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2019.123649