A van der Corput-type lemma for power bounded operators
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-016-1701-2
Abstract: We prove a van der Corput-type lemma for power bounded Hilbert space operators. As a corollary we show that $$N^{-1}\sum _{n=1}^N T^{p(n)}$$N-1∑n=1NTp(n) converges in the strong operator topology for all power bounded Hilbert space operators… read more here.
Keywords: van der; der corput; corput type; power ... See more keywords
MULTIDIMENSIONAL VAN DER CORPUT SETS AND SMALL FRACTIONAL PARTS OF POLYNOMIALS
Sign Up to like & getrecommendations! Published in 2019 at "Mathematika"
DOI: 10.1112/s0025579318000529
Abstract: We establish Diophantine inequalities for the fractional parts of generalized polynomials $f$, in particular for sequences $\nu(n)=\lfloor n^c\rfloor+n^k$ with $c>1$ a non-integral real number and $k\in\mathbb{N}$, as well as for $\nu(p)$ where $p$ runs through… read more here.
Keywords: van der; der corput; corput sets; multidimensional van ... See more keywords