Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSchur parameters and Caratheodory class
82
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The Schur (resp. Caratheodory) class consists of all the analytic functions $f$ on the unit disk with $|f|le 1$ (resp. $Re f>0$ and $f(0)=1$). The Schur parameters $gamma_0,gamma_1,dots (|gamma_j|le 1)$ are known to parametrize the coefficients of functions in the Schur class. By employing a recursive formula for it, we describe the $n$-th coefficient of a Caratheodory function in terms of $n$ independent variables $gamma_1,dots, gamma_n$ with $|gamma_j|le 1.$ The mapping properties of those correspondences are also studied.
rate research
Read More
We give several new characterizations of Caratheodory convergence of simply connected domains. We then investigate how different definitions of convergence generalize to the multiply-connected case.
The Kohn-Nireberg domains are unbounded domains in the complex Euclidean space of dimension 2 upon which many outstanding questions are yet to be explored. The primary aim of this article is to demonstrate that the Bergman and Caratheodory metrics of any Kohn-Nirenberg domains are positive and complete.
It is proved that for any domain in $mathbb C^n$ the Caratheodory--Eisenman volume is comparable with the volume of the indicatrix of the Caratheodory metric up to small/large constants depending only on $n.$ Then the multidimensional Suita conjecture theorem of Blocki and Zwonek implies a comparable relationship between these volumes and the Bergman kernel.
We introduce the Schur class of functions, discrete analytic on the integer lattice in the complex plane. As a special case, we derive the explicit form of discrete analytic Blaschke factors and solve the related basic interpolation problem.
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers $kappa_1, ldots, kappa_N$, quaternions $p_1, ldots, p_N$ all of modulus $1$, so that the $2$-spheres determined by each point do not intersect and $p_u eq 1$ for $u = 1,ldots, N$, and quaternions $s_1, ldots, s_N$, we wish to find a slice hyperholomorphic Schur function $s$ so that $$lim_{substack{rrightarrow 1 rin(0,1)}} s(r p_u) = s_uquad {rm for} quad u=1,ldots, N,$$ and $$lim_{substack{rrightarrow 1 rin(0,1)}}frac{1-s(rp_u)overline{s_u}}{1-r}lekappa_u,quad {rm for} quad u=1,ldots, N.$$ Our arguments relies on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
