Analysis and Operator Theory Seminar - Vladimir Eiderman

August 12, 2019
Tuesday, September 24, 2019 - 2:00pm to 3:00pm
Cockins Hall 240
photo of 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.

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