Geometry of the symmetrized polydisc
نویسندگان
چکیده
منابع مشابه
Estimates of the Carathéodory Metric on the Symmetrized Polydisc
Estimates for the Carathéodory metric on the symmetrized polydisc are obtained. It is also shown that the Carathéodory and Kobayashi distances of the symmetrized three-disc do not coincide.
متن کاملInterpolating Sequences in the Polydisc
Let H°°(Dn) denote the set of all bounded analytic functions defined on the polydisc D" of Cn. In this note, we give a sufficient condition for sequences of points in £>" to be interpolating sequences for H°°(Dn). We also discuss some conditions for interpolation of general domains. Let G(X) be the set of all bounded continuous functions on a compact set X and let A C C(X) be a uniform algebra ...
متن کاملThe //"-corona Theorem for the Polydisc
Let Hp = Hp(D") denote the usual Hardy spaces on the polydisc D" . We prove in this paper the following theorem: Suppose f\, fa, ... , fit € H°° , \\fj\\Hoo <\,and Y.%\ \fj(z)\ > S > 0. Then for every g in HP , 1 < p < oo, there are Hp functions g, g, ... , gm such that 2~2T=\ fj(z)Sj(z) = g(z). Moreover, we have ||g/||//p < c(m, n, S , p)\\g\\np . (When p = 2, n = 1 , this theorem is known to ...
متن کاملOptimal shaping properties of the truncated polydisc
induced by the linear feedback scheme X; = BjY " + y " , j = 1,2;.., m, that may be used to characterize the capacity region. The general outer bound of Section 111 ((19)) might be relevant here. This technique may also provide insight in determining the capacity region of general m-user Gaussian white noise multiple access channels with feedback. (0 = h (2 "). (All Here (i) is the chain rule, ...
متن کاملPositive Carath Eodory Interpolation on the Polydisc
The positive Carath eodory interpolation problem in the Agler-Herglotz class on the polydisc is solved, along with a several variable version of the Naimark dila-tion theorem. In addition, the positive Carath eodory interpolation problem for general holomorphic functions is discussed and numerical results are presented.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2005
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-004-1183-z