Spectral versus classical Nevanlinna-Pick interpolation in dimension two
نویسنده
چکیده
A genericity condition is removed from a result of Agler and Young which reduces the spectral Nevanlinna-Pick problem in two dimensions to a family of classical Nevanlinna-Pick problems. Unlike the original approach, the argument presented here does not involve state-space methods.
منابع مشابه
Ela Spectral versus Classical Nevanlinna-pick Interpolation in Dimension Two∗
A genericity condition is removed from a result of Agler and Young which reduces the spectral Nevanlinna-Pick problem in two dimensions to a family of classical Nevanlinna-Pick problems. Unlike the original approach, the argument presented here does not involve state-space methods.
متن کاملNonisotropically Balanced Domains, Lempert Function Estimates, and the Spectral Nevanlinna-pick Problem
We introduce the notion of a Λ-nonisotropically balanced domain and show that the symmetrized polydisc in Cn, n ≥ 2, is an example of such a domain. Given a Λ-nonisotropically balanced domain Ω, we derive effective estimates from above and from below for the Lempert function κ̃Ω at (0, z) ∈ Ω × Ω. We use these estimates to derive certain conditions for realising a two-point Nevanlinna-Pick inter...
متن کاملSpectral Factorization and Nevanlinna - Pick Interpolation *
We develop a spectral factorization algorithm based on linear fractional transformations and on the Nevanlinna-Pick interpolation theory. The algorithm is recursive and depends on a choice of points (Zk, k 1, 2, ") inside the unit disk. Under a mild condition on the distribution of the zk's, the convergence of the algorithm is established. The algorithm is flexible and convergence can be influe...
متن کاملA Fast Algorithm for Matrix-Valued Nevanlinna-Pick Interpolation
In this paper, we derive a new fast algorithm for the matrixvalued Nevanlinna-Pick interpolation. Given n distinct points zi in the unit disk jzj < 1 and n complex matrices Wk of dimension m m, satisfying the Pick condition for 1 k n, the new Nevanlinna-Pick interpolation algorithm requires only 20 3 nm 3 complex arithmetic operations to evaluate the matrix-valued interpolatory rational functio...
متن کاملSpectral Lifting in Banach Algebras and Interpolation in Several Variables
Let A be a unital Banach algebra and let J be a closed two-sided ideal of A. We prove that if any invertible element of A/J has an invertible lifting in A, then the quotient homomorphism Φ : A → A/J is a spectral interpolant. This result is used to obtain a noncommutative multivariable analogue of the spectral commutant lifting theorem of Bercovici, Foiaş, and Tannenbaum. This yields spectral v...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017