Zobrazeno 1 - 10
of 200
pro vyhledávání: '"Petrov, F."'
Autor:
Krachun, D., Petrov, F.
We prove an asymptotically tight lower bound on $|A+\lambda A|$ for $A\subset \mathbb{C}$ and algebraic integer $\lambda$. The proof combines strong version of Freiman's theorem, structural theorem on dense subsets of a hypercubic lattice and a gener
Externí odkaz:
http://arxiv.org/abs/2311.09399
Autor:
Vershik, A., Petrov, F.
Publikováno v:
Functional Analysis and its Applications, v 57,#1,2023
A notion of the limit spectral measure of a metric triple (i.e., a metric measure space) is defined. If the metric is square integrable, then the limit spectral measure is deterministic and coinsides with the spectrum of the integral operator in $L^2
Externí odkaz:
http://arxiv.org/abs/2306.14883
Autor:
Vershik, A., Petrov, F.
We define a class of continuous graded graphs similar to the graph of Gelfand--Tsetlin patterns, and describe the set of all ergodic central measures of discrete type on the path spaces of such graphs. The main observation is that an ergodic central
Externí odkaz:
http://arxiv.org/abs/2209.11733
Autor:
Petrov, F.
Landau function $g(n)$ is the maximal possible least common multiple of several positive integers with sum not exceeding $n$. Under additional assumptions that these numbers are the differences of disjoint bi-infinite arithmetic progressions the maxi
Externí odkaz:
http://arxiv.org/abs/2209.07362
Autor:
Bochkov, I. A., Petrov, F. V.
Let $(\mathcal{P},\leqslant)$ be a finite poset. Define the numbers $a_1,a_2,\ldots$ (respectively, $c_1,c_2,\ldots$) so that $a_1+\ldots+a_k$ (respectively, $c_1+\ldots+c_k$) is the maximal number of elements of $\mathcal{P}$ which may be covered by
Externí odkaz:
http://arxiv.org/abs/2001.03670
For a positive integer $n>1$ denote by $\omega(n)$ the maximal possible number $k$ of different functions $f_1,\dots,f_k:\mathbb{Z}/n\mathbb{Z}\mapsto \mathbb{Z}/n\mathbb{Z}$ such that each function $f_i-f_j,i
Externí odkaz:
http://arxiv.org/abs/1901.00440
Autor:
Gordon, J., Petrov, F.
Let $\rho$ be a metric on the set $X=\{1,2,\dots,n+1\}$. Consider the $n$-dimensional polytope of functions $f:X\rightarrow \mathbb{R}$, which satisfy the conditions $f(n+1)=0$, $|f(x)-f(y)|\leq \rho(x,y)$. The question on classifying metrics dependi
Externí odkaz:
http://arxiv.org/abs/1608.06848
Classical theorem of Luzin states that a measurable function of one real variable is "almost" continuous. For measurable functions of several variables the analogous statement (continuity on the product of sets having almost full measure) does not ho
Externí odkaz:
http://arxiv.org/abs/1410.0898
Autor:
Petrov, F.1 (AUTHOR) fedyapetrov@gmail.com
Publikováno v:
Acta Mathematica Hungarica. Feb2023, Vol. 169 Issue 1, p272-276. 5p.
Publikováno v:
CEMJ-2013
We study a wide class of metrics in a Lebesgue space with a standard measure, the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the "-entropy of a
Externí odkaz:
http://arxiv.org/abs/1205.1174