Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Igor Chyzhykov"'
Publikováno v:
Journal of the Australian Mathematical Society. :1-27
It is known that, in the unit disc as well as in the whole complex plane, the growth of the analytic coefficients $A_0,\dotsc ,A_{k-2}$ of $$ \begin{align*} f^{(k)} + A_{k-2} f^{(k-2)} + \dotsb + A_1 f'+ A_0 f = 0, \quad k\geqslant 2, \end{align*} $$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ef1cd4abd7f2b775ec881da0192fe986
https://doi.org/10.1017/s1446788722000118
https://doi.org/10.1017/s1446788722000118
Publikováno v:
Journal de Mathématiques Pures et Appliquées. 160:158-201
It is shown that the order and the lower order of growth are equal for all non-trivial solutions of $f^{(k)}+A f=0$ if and only if the coefficient $A$ is analytic in the unit disc and $\log^+ M(r,A)/\log(1-r)$ tends to a finite limit as $r\to 1^-$. A
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a551b8f87b130440ec049eb6fb2aacdf
https://doi.org/10.1016/j.matpur.2022.02.001
https://doi.org/10.1016/j.matpur.2022.02.001
Autor:
Jianren Long, Igor Chyzhykov
Publikováno v:
Proceedings of the Edinburgh Mathematical Society. 64:247-261
Let $(z_k)$ be a sequence of distinct points in the unit disc $\mathbb{D}$ without limit points there. We are looking for a function $a(z)$ analytic in $\mathbb{D}$ and such that possesses a solution having zeros precisely at the points $z_k$, and th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::42340c6e88f39b400d97db660ed4e561
https://doi.org/10.1017/s0013091521000122
https://doi.org/10.1017/s0013091521000122
Autor:
Igor Chyzhykov
Publikováno v:
Israel Journal of Mathematics. 236:931-957
We propose a new approach for studying asymptotic behaviour of pth means of the logarithmic potential and classes of analytic and subharmonic functions in the unit disc. In particular, we generalize a criterion due to G. MacLane and L. Rubel of bound
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::23057d3702913d18d410dfad4019365c
https://doi.org/10.1007/s11856-020-1996-x
https://doi.org/10.1007/s11856-020-1996-x
Publikováno v:
European Journal of Mathematics. 6:1-3
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4711429e285bc9e99fb13b011ddfed21
https://doi.org/10.1007/s40879-020-00399-9
https://doi.org/10.1007/s40879-020-00399-9
Autor:
Galyna Beregova, Igor Chyzhykov
Publikováno v:
Analysis and Mathematical Physics. 9:809-820
We study non-regularity of growth of the fractional Cauchy transform $$\begin{aligned} f(z)=\int _{-\pi }^{\pi } \frac{d\psi (t)}{(1-ze^{-it})^\alpha }, \quad \alpha >0, \psi \in BV[-\pi ,\pi ], \end{aligned}$$ in terms of the modulus of continuity o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::316a8afaecc65919485421595d30aa72
https://doi.org/10.1007/s13324-019-00317-7
https://doi.org/10.1007/s13324-019-00317-7
Autor:
Jianren Long, Igor Chyzhykov
Publikováno v:
Trends in Mathematics ISBN: 9783030744168
We are looking for a function a(z) analytic in the unit disc such that \(f''+a(z)f= 0\) possesses a solution having zeros precisely at the points \(z_k\), and the resulting function a(z) has ‘minimal’ growth.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e8923dda676aed53e0ca16f740e4594d
https://doi.org/10.1007/978-3-030-74417-5_10
https://doi.org/10.1007/978-3-030-74417-5_10
We introduce a concept of a quasi proximate order which is a generalization of a proximate order and allows us to study efficiently analytic functions whose order and lower order of growth are different. We prove an existence theorem of a quasi proxi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::42ff16cd4fb0afe4df6ae5c66b9108ee
Autor:
Igor Chyzhykov, M. Voitovych
Publikováno v:
Complex Variables and Elliptic Equations. 62:899-913
We describe the growth of pth means, , of the invariant Green potential in the unit ball in in terms of smoothness properties of a measure. In particular, a criterion of boundedness of pth means of the potential is obtained, a result of M. Stoll is g
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3720f841defaf1c5bff5b48ee810efd2
https://doi.org/10.1080/17476933.2016.1251423
https://doi.org/10.1080/17476933.2016.1251423
Autor:
Igor Chyzhykov, M. Kravets
Publikováno v:
Computational Methods and Function Theory. 16:53-64
We study the behavior of the minimum modulus of analytic functions in the unit disc in terms of \(\rho _\infty \)-order, which is the limit of the orders of \(L_p\)-norms of \(\log |f(re^{i\theta })|\) over the circle as \(p\rightarrow \infty \). Thi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::002918b9f6a1fea05874311500cc148d
https://doi.org/10.1007/s40315-015-0118-y
https://doi.org/10.1007/s40315-015-0118-y