arXiv subjects

Olena Kozhushkina

Publications and source records attributed to Olena Kozhushkina.

3 recordsLinked to original sources

arXiv2023

The $p$-Adic Valuation Trees for Quadratic Polynomials for Odd Primes

We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations. Under this representation, a finite tree corresponds to a periodic sequence, and an infinite tree corresponds to an unbounded sequence. We use the polynomial coefficients to determine whether the $p$-adic valuation trees are finite or infinite, the number of infinite branches, the number of levels, the valuations at terminating nodes, and their relationship to the corresponding sequences.

math.NT↗

arXiv2021

2-adic Valuations of Quadratic Sequences

Properties of 2-adic valuation sequences for general quadratic polynomials with integer coefficients are determined directly from the coefficients. These properties include boundedness or unboundedness, periodicity, and valuations at terminating nodes. We completely describe the periodic sequences in the bounded case. Throughout, we frame results in terms of trees and sequences.

math.NT↗

arXiv2013

The Bishop-Phelps-Bollobás property for numerical radius in $\ell_1(\mathbb{C})$

We show that the set of bounded linear operators from $X$ to $X$ admits a Bishop-Phelps-Bollobás type theorem for numerical radius whenever $X$ is $\ell_1(\mathbb{C})$ or $c_0(\mathbb{C})$. As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollobás theorem for $\ell_1(\mathbb{C})$.

math.FA↗