Zobrazeno 1 - 10
of 83
pro vyhledávání: '"Vishnyakova, Anna"'
Elementary, but very useful lemma due to Biernacki and Krzy\.{z} (1955) asserts that the ratio of two power series inherits monotonicity from that of the sequence of ratios of their corresponding coefficients. Over the last two decades it has been re
Externí odkaz:
http://arxiv.org/abs/2408.01755
For a given real polynomial $p$ we study the possible number of real roots of a differential polynomial $H_{\varkappa}[p](x) = \varkappa\left(p'(x)\right)^2-p(x)p''(x), \varkappa \in \mathbb{R}.$ In the special case when all real zeros of the polynom
Externí odkaz:
http://arxiv.org/abs/2406.00686
In this paper, we prove a number of results providing either necessary or sufficient conditions guaranteeing that the number of real roots of real polynomials of a given degree is either less or greater than a given number. We also provide counterexa
Externí odkaz:
http://arxiv.org/abs/2403.12200
Autor:
Katkova, Olga, Vishnyakova, Anna
A real sequence $(b_k)_{k=0}^\infty$ is called totally positive if all minors of the infinite matrix $ \left\| b_{j-i} \right\|_{i, j =0}^\infty$ are nonnegative (here $b_k=0$ for $k<0$). In this paper, we investigate the problem of description of th
Externí odkaz:
http://arxiv.org/abs/2402.05017
We study the growth of the resolvent of a Toeplitz operator $T_b$, defined on the Hardy space, in terms of the distance to its spectrum $\sigma(T_b)$. We are primarily interested in the case when the symbol $b$ is a Laurent polynomial (\emph{i.e., }
Externí odkaz:
http://arxiv.org/abs/2401.12095
Autor:
Nguyen, Thu Hien, Vishnyakova, Anna
We find the intervals $[\alpha, \beta (\alpha)]$ such that if a univariate real polynomial or entire function $f(z) = a_0 + a_1 z + a_2 z^2 + \cdots $ with positive coefficients satisfy the conditions $ \frac{a_{k-1}^2}{a_{k-2}a_{k}} \in [\alpha, \be
Externí odkaz:
http://arxiv.org/abs/2212.05692
We find the constant $b_{\infty}$ ($b_{\infty} \approx 4.81058280$) such that if a complex polynomial or entire function $f(z) = \sum_{k=0}^ \omega a_k z^k, $ $\omega \in \{2, 3, 4, \ldots \} \cup \{\infty\},$ with nonzero coefficients satisfy the co
Externí odkaz:
http://arxiv.org/abs/2207.08108
Autor:
Nguyen, Thu Hien, Vishnyakova, Anna
We study the entire functions $f(z) = \sum_{k=0}^\infty a_k z^k, a_k>0,$ with non-monotonic second quotients of Taylor coefficients, namely, such that $\frac{a_{2m-1}^2}{a_{2m-2}a_{2m}} = a>1$ and $\frac{a_{2m}^2}{a_{2m-1}a_{2m+1}} = b>1$ for all $m
Externí odkaz:
http://arxiv.org/abs/2107.13061
Autor:
Nguyen, Thu Hien, Vishnyakova, Anna
For an entire function $f(z) = \sum_{k=0}^\infty a_k z^k,$ $a_k >0,$ we define the sequence of the second quotients of Taylor coefficients $Q := \left( \frac{a_k^2}{a_{k-1}a_{k+1}} \right)_{k=1}^\infty$. We find new necessary conditions for a functio
Externí odkaz:
http://arxiv.org/abs/2101.11757
Autor:
Nguyen, Thu Hien, Vishnyakova, Anna
We prove that if $f(x) = \sum_{k=0}^\infty a_k x^k,$ $a_k >0, $ is an entire function such that the sequence $Q := \left( \frac{a_k^2}{a_{k-1}a_{k+1}} \right)_{k=1}^\infty$ is non-decreasing and $\frac{a_1^2}{a_{0}a_{2}} \geq 2\sqrt[3]{2},$ then all
Externí odkaz:
http://arxiv.org/abs/2008.04754