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Creators/Authors contains: "Richter, Florian"

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  1. ; ; (, Proceedings of the American Mathematical Society, Series B)
    Let ( G / Γ<#comment/> , R a ) (G/\Gamma ,R_a) be an ergodic k k -step nilsystem for k ≥<#comment/> 2 k\geq 2 . We adapt an argument of Parry [Topology 9 (1970), pp. 217–224] to show that L 2 ( G / Γ<#comment/> ) L^2(G/\Gamma ) decomposes as a sum of a subspace with discrete spectrum and a subspace of Lebesgue spectrum with infinite multiplicity. In particular, we generalize a result previously established by Host–Kra–Maass [J. Anal. Math.124(2014), pp. 261–295] for 2 2 -step nilsystems and a result by Stepin [Uspehi Mat. Nauk24(1969), pp. 241–242] for nilsystems G / Γ<#comment/> G/\Gamma with connected, simply connected G G . 
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  2. ; ; ; (, Communications of the American Mathematical Society)
    We show that every set A A of natural numbers with positive upper Banach density can be shifted to contain the restricted sumset { b 1 + b 2 : b 1 , b 2 ∈<#comment/> B  and  b 1 ≠<#comment/> b 2 } \{b_1 + b_2 : b_1, b_2\in B \text { and } b_1 \ne b_2 \} for some infinite set B ⊂<#comment/> A B \subset A . 
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  3. ; ; ; ; (, IEEE)
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  5. ; ; ; (, International mathematics research notices)
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  6. ; ; ; (, Journal of the American Mathematical Society)
    Motivated by questions asked by Erdős, we prove that any set A ⊂<#comment/> N A\subset \mathbb {N} with positive upper density contains, for any k ∈<#comment/> N k\in \mathbb {N} , a sumset B 1 + ⋯<#comment/> + B k B_1+\cdots +B_k , where B 1 B_1 , …, B k ⊂<#comment/> N B_k\subset \mathbb {N} are infinite. Our proof uses ergodic theory and relies on structural results for measure preserving systems. Our techniques are new, even for the previously known case of k = 2 k=2 . 
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  7. ; ; (, IEEE)
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  8. ; ; (, Mathematical Research Letters)
    In this work we study the set of eventually always hitting points in shrinking target systems. These are points whose long orbit segments eventually hit the corresponding shrinking targets for all future times. We focus our attention on systems where translates of targets exhibit near perfect mutual independence, such as Bernoulli schemes and the Gauß map. For such systems, we present tight conditions on the shrinking rate of the targets so that the set of eventually always hitting points is a null set (or co-null set respectively). 
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  9. ; ; ; ; ; ; (, IEEE)
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