arXiv subjects

L. M. Arutyunyan

Publications and source records attributed to L. M. Arutyunyan.

2 recordsLinked to original sources

arXiv2019

Integral Remez inequalities for polynomials on convex bodies

We denote as an integral Remez inequality an inequality of the form $$ \|f\|_{L^{1}(μ)} \le C(Ω,μ(A), X) \|f\|_{L^{1}(μ_{A})}, $$ where $μ_A$ is the normalised restriction of a measure $μ$ to a set $A$. Let $μ$ be the uniform distribution over a convex body A and $f$ be a polynomial of degree $d$. One can choose $C$ independent of the dimension of the set A, in contrast with a classical $L^{\infty}$ Remez inequality.

math.FA↗

arXiv2018

On growth of the number of determinants with restricted entries

Let $A$ be a finite subset of a field $\mathbb{F}$ and $D_n(A)$ be a set of all matrices with entries in $A$, namely $$ D_n(A)=\{D\in \mathbb{F}\ |\ \exists a_{ij}\in A, 1 \le i,j \le n, \det\bigl((a_{ij})\bigr)=D\}, $$ where the symbol $(a_{ij})$ defines the matrix with elements $a_{ij}$. How big is the size of the set $D_n(A)$ comparing to the size of the set $A$?

math.NT↗