The Experts below are selected from a list of 1599 Experts worldwide ranked by ideXlab platform
Stephane Seuret - One of the best experts on this subject based on the ideXlab platform.
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a localized jarnik Besicovitch theorem
Advances in Mathematics, 2011Co-Authors: Julien Barral, Stephane SeuretAbstract:Abstract Fundamental questions in Diophantine approximation are related to the Hausdorff dimension of sets of the form { x ∈ R : δ x = δ } , where δ ⩾ 1 and δ x is the Diophantine approximation exponent of an irrational number x. We go beyond the classical results by computing the Hausdorff dimension of the sets { x ∈ R : δ x = f ( x ) } , where f is a continuous function. Our theorem applies to the study of the approximation exponents by various approximation families. It also applies to functions f which are continuous outside a set of prescribed Hausdorff dimension.
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a localized jarnik Besicovitch theorem
arXiv: Number Theory, 2009Co-Authors: Julien Barral, Stephane SeuretAbstract:Fundamental questions in Diophantine approximation are related to the Hausdorff dimension of sets of the form $\{x\in \mathbb{R}: \delta_x = \delta\}$, where $\delta \geq 1$ and $\delta_x$ is the Diophantine approximation rate of an irrational number $x$. We go beyond the classical results by computing the Hausdorff dimension of the sets $\{x\in\mathbb{R}: \delta_x =f(x)\}$, where $f$ is a continuous function. Our theorem applies to the study of the approximation rates by various approximation families. It also applies to functions $f$ which are continuous outside a set of prescribed Hausdorff dimension.
Litvinov Semyon - One of the best experts on this subject based on the ideXlab platform.
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Noncommutative almost uniform Wiener-Wintner ergodic theorem
2020Co-Authors: Chilin Vladimir, Litvinov SemyonAbstract:Almost uniform version of noncommutative Wiener-Wintner ergodic theorem and its extension to Besicovitch weights are proved.Comment: There is a critical error in Proposition 2.
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Almost uniform convergence in Wiener-Wintner ergodic theorem
2020Co-Authors: Chilin Vladimir, Litvinov SemyonAbstract:We extend almost everywhere convergence in Wiener-Wintner ergodic theorem for $\sigma$-finite measure to a generally stronger almost uniform convergence and present a larger, universal, space for which this convergence holds. We then extend this result to the case with Besicovitch weights
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Noncommutative weighted individual ergodic theorems with continuous time
2018Co-Authors: Chilin Vladimir, Litvinov SemyonAbstract:We show that ergodic flows in noncommutative fully symmetric spaces (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford-Schwartz operators and modulated by bounded Besicovitch almost periodic functions converge almost uniformly. The corresponding local ergodic theorem is also discussed
Ilkka Törmä - One of the best experts on this subject based on the ideXlab platform.
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geometry and dynamics of the Besicovitch and weyl spaces
Developments in Language Theory, 2012Co-Authors: Ville Salo, Ilkka TörmäAbstract:We study the geometric properties of Cantor subshifts in the Besicovitch space, proving that sofic shifts occupy exactly the homotopy classes of simplicial complexes. In addition, we study continuous functions that locally look like cellular automata and present a new proof for the nonexistence of transitive cellular automata in the Besicovitch space.
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Geometry and Dynamics of the Besicovitch and Weyl Spaces
arXiv: Dynamical Systems, 2012Co-Authors: Ville Salo, Ilkka TörmäAbstract:We study the geometric properties of Cantor subshifts in the Besicovitch space, proving that sofic shifts occupy exactly the homotopy classes of simplicial complexes. In addition, we study canonical projections into subshifts, characterize the cellular automata that are contracting or isometric in the Besicovitch or Weyl spaces, study continuous functions that locally look like cellular automata, and present a new proof for the nonexistence of transitive cellular automata in the Besicovitch space.
Marianna Csornyei - One of the best experts on this subject based on the ideXlab platform.
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The Kakeya needle problem and the existence of Besicovitch and Nikodym sets for rectifiable sets
Proceedings of The London Mathematical Society, 2018Co-Authors: Alan Chang, Marianna CsornyeiAbstract:We solve the Kakeya needle problem and construct a Besicovitch and a Nikodym set for rectifiable sets.
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the Besicovitch federer projection theorem is false in every infinite dimensional banach space
Israel Journal of Mathematics, 2017Co-Authors: David Bate, Marianna Csornyei, Bobby WilsonAbstract:We construct a purely unrectifiable set of finite H 1-measure in every infinite-dimensional separable Banach space X whose image under every 0 ≠ x* ∈ X* has positive Lebesgue measure. This demonstrates completely the failure of the Besicovitch–Federer projection theorem in infinitedimensional Banach spaces.
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the Besicovitch federer projection theorem is false in every infinite dimensional banach space
arXiv: Functional Analysis, 2015Co-Authors: David Bate, Marianna Csornyei, Bobby WilsonAbstract:We construct a purely unrectifiable set of finite $\mathcal H^1$-measure in every infinite dimensional separable Banach space $X$ whose image under every $0\neq x^*\in X^*$ has positive Lebesgue measure. This demonstrates completely the failure of the Besicovitch-Federer projection theorem in infinite dimensional Banach spaces.
Julien Barral - One of the best experts on this subject based on the ideXlab platform.
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a localized jarnik Besicovitch theorem
Advances in Mathematics, 2011Co-Authors: Julien Barral, Stephane SeuretAbstract:Abstract Fundamental questions in Diophantine approximation are related to the Hausdorff dimension of sets of the form { x ∈ R : δ x = δ } , where δ ⩾ 1 and δ x is the Diophantine approximation exponent of an irrational number x. We go beyond the classical results by computing the Hausdorff dimension of the sets { x ∈ R : δ x = f ( x ) } , where f is a continuous function. Our theorem applies to the study of the approximation exponents by various approximation families. It also applies to functions f which are continuous outside a set of prescribed Hausdorff dimension.
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a localized jarnik Besicovitch theorem
arXiv: Number Theory, 2009Co-Authors: Julien Barral, Stephane SeuretAbstract:Fundamental questions in Diophantine approximation are related to the Hausdorff dimension of sets of the form $\{x\in \mathbb{R}: \delta_x = \delta\}$, where $\delta \geq 1$ and $\delta_x$ is the Diophantine approximation rate of an irrational number $x$. We go beyond the classical results by computing the Hausdorff dimension of the sets $\{x\in\mathbb{R}: \delta_x =f(x)\}$, where $f$ is a continuous function. Our theorem applies to the study of the approximation rates by various approximation families. It also applies to functions $f$ which are continuous outside a set of prescribed Hausdorff dimension.