Doğan Çömez
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View article: Quantization for Infinite Affine Transformations
Quantization for Infinite Affine Transformations Open
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system o…
View article: Individual ergodic theorems for infinite measure
Individual ergodic theorems for infinite measure Open
Given a $σ$-finite infinite measure space $(Ω,μ)$, it is shown that any Dunford-Schwartz operator $T:\,\mathcal L^1(Ω)\to\mathcal L^1(Ω)$ can be uniquely extended to the space $\mathcal L^1(Ω)+\mathcal L^\infty(Ω)$. This allows to find the…
View article: Optimal quantization for the condensation system associated with self-similar measures
Optimal quantization for the condensation system associated with self-similar measures Open
Let $S_1, S_2, T_1, T_2$ be contractive similarity mappings such that $S_1(x)=\frac 15 x$, $S_2(x)=\frac 1 5 x+\frac 45$, $T_1(x)=\frac 1{3} x+\frac 4{15}$, and $T_2(x)=\frac 1{3} x+\frac 25$ for all $x\in\mathbb R$. Set $P=\frac 13 P \cir…
View article: Canonical sequences of optimal quantization for condensation measures
Canonical sequences of optimal quantization for condensation measures Open
We consider condensation measures of the form $P:=\frac 13 P\circ S_1^{-1}+ \frac 13 P\circ S_2^{-1}+ \frac 13 ν$ associated with the system $(\mathcal{S}, (\frac 13, \frac 13, \frac 13), ν) , $ where $\mathcal{S}=\{S_i\}_{i=1}^2 $ are con…
View article: Pointwise ergodic theorems in symmetric spaces of measurable functions
Pointwise ergodic theorems in symmetric spaces of measurable functions Open
For a Dunford-Schwartz operator in a fully symmetric space of measurable functions of an arbitrary measure space, we prove pointwise convergence of the conventional and weighted ergodic averages.
View article: Quantization of probability distributions on R-triangles
Quantization of probability distributions on R-triangles Open
In this paper, we have considered a Borel probability measure $P$ on $\mathbb R^2$ which has support the R-triangle generated by a set of three contractive similarity mappings on $\mathbb R^2$. For this probability measure, the optimal set…
View article: Quantization for uniform distributions on stretched Sierpi\\'nski\n triangles
Quantization for uniform distributions on stretched Sierpi\\'nski\n triangles Open
In this paper, we have considered a uniform probability distribution\nsupported by a stretched Sierpi\\'nski triangle. For this probability measure,\nthe optimal sets of $n$-means and the $n$th quantization errors are determined\nfor all $…
View article: Quantization for infinite affine transformations
Quantization for infinite affine transformations Open
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system o…
View article: Probability distributions supported on sets generated by infinite affine transformations and optimal quantization
Probability distributions supported on sets generated by infinite affine transformations and optimal quantization Open
Quantization of a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this paper, a probability distribution is considered which is generated by an infinite …
View article: Quantization for uniform distributions on Sierpi\'nski carpets with strong separation condition
Quantization for uniform distributions on Sierpi\'nski carpets with strong separation condition Open
Let $P$ be a Borel probability measure on $\mathbb R^2$ supported by the Sierpi\'nski carpet generated by a set of four contractive similarity mappings satisfying the strong separation condition. For this probability measure, we determine …
View article: Quantization for uniform distributions of Cantor dusts on $\mathbb{R}^2$
Quantization for uniform distributions of Cantor dusts on $\mathbb{R}^2$ Open
Let $P$ be a Borel probability measure on $\mathbb R^2$ supported by the Cantor dusts generated by a set of $4^u,\ u\geq 1$, contractive similarity mappings satisfying the strong separation condition. For this probability measure, we deter…
View article: Optimal quantizers for probability distributions on Sierpi\'nski carpets
Optimal quantizers for probability distributions on Sierpi\'nski carpets Open
In this paper, we investigate the optimal sets of $n$-means and the $n$th quantization error for singular continuous probability measures on $\mathbb R^2$ supported by Sierpi\'nski carpets. Utilizing the geometric structure of Sierpi\'nski…
View article: Quantization of the probability distribution on the Sierpi\'nski carpet
Quantization of the probability distribution on the Sierpi\'nski carpet Open
Quantization of a probability distribution is the process of estimating a given probability by a discrete probability that assumes only a finite number of levels in its support. Let $P$ be a Borel probability measure on $\mathbb R^2$ which…
View article: On pointwise ergodic theorems for infinite measure
On pointwise ergodic theorems for infinite measure Open
For a Dunford-Schwartz operator in the $L^p-$space, $1\leq p< \infty$ , of an arbitrary measure space, we prove pointwise convergence of the conventional and Besicovitch weighted ergodic averages. Pointwise convergence of various types of …
View article: Good modulating sequences for the ergodic Hilbert transform
Good modulating sequences for the ergodic Hilbert transform Open
This article investigates classes of bounded sequences of complex numbers that are universally good for the ergodic Hilbert transform in L_p-spaces, 2\leq p\leq \infty : The class of bounded Besicovitch sequences satisfying a rate conditio…