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Analysis and Operator Theory Seminar - Vladimir Eiderman

photo of Vladimir Eiderman
September 24, 2019
2:00PM - 3:00PM
Cockins Hall 240

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Add to Calendar 2019-09-24 14:00:00 2019-09-24 15:00:00 Analysis and Operator Theory Seminar - Vladimir Eiderman Title: A "rare" plane set with Hausdorff dimension 2 Speaker: Vladimir Eiderman (Indiana University) Abstract: We prove that for every at most countable family $\{f_k(x)\}$ of real functions on $[0,1)$ there is a single-valued real function $F(x)$, $x\in[0,1)$, such that the Hausdorff dimension of the graph $\Gamma$ of $F(x)$ equals 2, and for every $C\in\mathbb{R}$ and every $k$, the intersection of $\Gamma$ with the graph of the function $f_k(x)+C$ consists of at most one point. We also construct a family of functions of cardinality continuum and a function $F$ with similar properties. Cockins Hall 240 Department of Mathematics math@osu.edu America/New_York public

Title: A "rare" plane set with Hausdorff dimension 2

Speaker: Vladimir Eiderman (Indiana University)

Abstract: We prove that for every at most countable family $\{f_k(x)\}$ of real functions on $[0,1)$ there is a single-valued real function $F(x)$, $x\in[0,1)$, such that the Hausdorff dimension of the graph $\Gamma$ of $F(x)$ equals 2, and for every $C\in\mathbb{R}$ and every $k$, the intersection of $\Gamma$ with the graph of the function $f_k(x)+C$ consists of at most one point. We also construct a family of functions of cardinality continuum and a function $F$ with similar properties.

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