Nir Lev

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20242026

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8 papers · 1 filter

math.CA2025

Schauder frames of discrete translates in $L^{2} (R)$

Nir Lev, Anton Tselishchev

We construct a uniformly discrete sequence ${I^»_{1} < I^»_{2} < \dots} \subset R$ and functions $g$ and ${g_{n}^{*}}$ in $L^{2} (R)$ , such that every $f \in L^2(\mathbb{…

math.CA2025

Schauder frames of discrete translates in $L^{p} (R)$

Nir Lev, Anton Tselishchev

For every $p > (1 + 5) /2$ we construct a uniformly discrete real sequence ${I^»_{n}}_{n = 1}^{\infty}$ satisfying $∣ I^»_{n} ∣ = n + o (1)$ , a function $g \in L^{p} (R)$ , and con…

math.CA2025

The TurÃ¡n and Delsarte problems and their duals

Mihail N. Kolountzakis, Nir Lev, MÃ¡tÃ© Matolcsi

We study two optimization problems for positive definite functions on Euclidean space with restrictions on their support and sign: the Turan problem and the Delsarte problem. These…

math.CA2025

Geometric implications of weak tiling

Mihail N. Kolountzakis, Nir Lev, MÃ¡tÃ© Matolcsi

The notion of weak tiling played a key role in the proof of Fuglede's spectral set conjecture for convex domains, due to the fact that every spectral set must weakly tile its compl…

math.CA2025

Unconditional Schauder frames of exponentials and of uniformly bounded functions in $L^{p}$ spaces

Nir Lev, Anton Tselishchev

It is known that there is no unconditional basis of exponentials in the space $L^{p} (I^c ◯)$ , $p \neq = 2$ , for any set $I^c ◯ \subset R^{d}$ of finite measure. This is a consequence of…

math.CA2025

Maximality and completeness of orthogonal exponentials on the cube

It is possible to have a packing by translates of a cube that is maximal (i.e.\ no other cube can be added without overlapping) but does not form a tiling. In the long running anal…

Schauder frames of discrete translates in L2(R)

Schauder frames of discrete translates in Lp(R)

The TurÃ¡n and Delsarte problems and their duals

Geometric implications of weak tiling

Unconditional Schauder frames of exponentials and of uniformly bounded functions in Lp spaces

Maximality and completeness of orthogonal exponentials on the cube

Schauder frames of discrete translates in $L^{2} (R)$

Schauder frames of discrete translates in $L^{p} (R)$

Unconditional Schauder frames of exponentials and of uniformly bounded functions in $L^{p}$ spaces