Related papers: Pick Interpolation for free holomorphic functions

In this paper we obtain a noncommutative multivariable analogue of the classical Nevanlinna-Pick interpolation problem for analytic functions with positive real parts on the open unit disc. As consequences, we deduce some results concerning…

We prove a new cross theorem for separately holomorphic functions.

We investigate the Pick problem for the polydisk and unit ball using dual algebra techniques. Some factorization results for Bergman spaces are used to describe a Pick theorem for any bounded region in $\mathbb{C}^d$.

There are three new things in this paper about the open symmetrized bidisk $\mathbb G = \{(z_1+z_2, z_1z_2) : |z_1|, |z_2| < 1\}$. They are motivated in the Introduction. In this Abstract, we mention them in the order in which they will be…

We give a characterization of interpolating sequences for bounded analytic functions on the bidisk.

We define a free holomorphic function to be a function that is locally a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization…

We prove that a suitably adjusted version of Peter Jones' formula for interpolation by bounded holomorphic functions gives a sharp upper bound for what is known as the constant of interpolation. We show how this leads to precise and…

We analyze the three point Pick interpolation problem on the bidisk

Interpolation Theory gives techniques for constructing spaces from two initial Banach spaces. We provide several conditions under which the restriction of a holomorphic map $f:X_0+X_1 \rightarrow Y_0+Y_1$ to the interpolated spaces (using…

We prove a noncommutative version of Bishop's peak interpolation-set theorem.

The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…

In this article, we establish a connection between Pick bodies and invariant functions. We demonstrate that an invariant function can be associated with any Pick body, which determines the solvability of a given Pick interpolation problem…

This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…

We deal with a problem of the reconstruction of any holomorphic function $f$ on the unit ball of $\mathbb{C}^2$ from its restricions on a union of complex lines. We give an explicit formula of Lagrange interpolation's type that is…

We treat interpolation for various logics.

In this article, we prove a decomposition theorem on differential polynomials of theta functions of high level.

In this paper we continue the study of free holomorphic functions on the unit ball of B(H)^n, where B(H) is the algebra of all bounded linear operators on a Hilbert space H. Several classical results from complex analysis have free…

We present a powerful theorem for proving the irreducibility of tempered unitary representations of the free group.

We show how Pick interpolation and interpolation on peak interpolation sets can be combined in an abstract uniform algebra setting. In particular as a special case, the Rudin-Carleson theorem can be combined with the classical Pick…

This note contains two new theorems about bounded holomorphic functions on the symmetrized bidisk -- a characterization of interpolating sequences and a Toeplitz corona theorem.