4 papers
Sampling and interpolation for analytic selfmappings of the disc
Nacho Monreal Galan, Michael Papadimitrakis
Two different problems are considered here. First, a characterization of sampling sequences for the class of analytic functions from the disc into itself is given. Second, a versio…
A variant of Hilbert's inequality and the norm of the Hilbert Matrix on
Vassilis Daskalogiannis, Petros Galanopoulos, Michael Papadimitrakis
We prove the nontrivial variant \[ \sum\limits_{m,n=1}^{\infty}\Big(\frac{n}{m}\Big)^{\frac{1}{q}-\frac{1}{p}}\frac{a_mb_n}{m+n-1}\leq\fracπ{\sin\fracπ{p}} \Big( \sum\limits_{m=1}^…
A class of non-convex polytopes that admit no orthonormal basis of exponentials
Mihail N. Kolountzakis, Michael Papadimitrakis
A conjecture of Fuglede states that a bounded measurable set D, of measure 1, can tile space by translations if and only if the Hilbert space L^2(D) has an orthonormal basis consis…
The Steinhaus tiling problem and the range of certain quadratic forms
Mihail N. Kolountzakis, Michael Papadimitrakis
We give a short proof of the fact that there are no measurable subsets of Euclidean space (in dimension d > 2), which, no matter how translated and rotated, always contain exactly…