منابع مشابه
Nevanlinna–pick Interpolation for Non-commutative Analytic Toeplitz Algebras
The non-commutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is us...
متن کاملLectures on Nevanlinna theory
Value distribution of a rational function f is controlled by its degree d, which is the number of preimages of a generic point. If we denote by n(a) the number of solutions of the equation f(z) = a, counting multiplicity, in the complex plane C, then n(a) ≤ d for all a ∈ C with equality for all a with one exception, namely a = f(∞). The number of critical points of f in C, counting multiplicity...
متن کاملComplete Nevanlinna-Pick Kernels
We give a new treatment of Quiggin’s and McCullough’s characterization of complete Nevanlinna-Pick kernels. We show that a kernel has the matrix-valued NevanlinnaPick property if and only if it has the vector-valued Nevanlinna-Pick property. We give a representation of all complete Nevanlinna-Pick kernels, and show that they are all restrictions of a universal complete Nevanlinna-Pick kernel.
متن کاملNevanlinna, Siegel, and Cremer
We study an irrationally indifferent cycle of points or circles of a rational function, which is either Siegel or Cremer by definition. We invent a new argument from the viewpoint of the Nevanlinna theory. Using this argument, we give a clear interpretation of some Diophantine quantity associated with an irrationally indifferent cycle. This quantity turns out to be Nevanlinnatheoretical. As a c...
متن کاملNevanlinna - Pick Interpolation For
We study the Nevanlinna-Pick problem for a class of subalgebras of H∞. This class includes algebras of analytic functions on embedded disks, the algebras of finite codimension in H∞ and the algebra of bounded analytic functions on a multiply connected domain. Our approach uses a distance formula that generalizes Sarason’s [18] work. We also investigate the difference between scalar-valued and m...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2001
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm147-3-4