The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The
authors then discuss the Pick problem of finding the function of smallest $ H^ infty $ norm …

Bohr's inequality says that if generators. We also include an application to Banach algebras.
We prove that every Banach algebra has an equivalent norm in which it satisfies a non …

We obtain an explicit representation formula and a Nevanlinna-Pick-type interpolation
theorem for the multiplier space of the reproducing kernel space ℌ (kd) of analytic functions …

The seminal 1989 work of Douglas and Paulsen on the theory of analytic Hilbert modules
precipitated a number of major research efforts. This in turn led to some intriguing and …

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 Nevanlinna–Pick …

We develop a theory of holomorphic functions in several noncommuting (free) variables and
provide a framework for the study of tuples of bounded linear operators on Hilbert spaces …

General results of interpolation (eg, Nevanlinna-Pick) by elements in the noncommutative
analytic Toeplitz algebra F∞(resp., noncommutative disc algebra A n) with consequences to …

This paper concerns unitary invariants for $ n $-tuples $ T:=(T_1,\ldots, T_n) $ of (not
necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces …

We study algebras of bounded, noncommutative (nc) analytic functions on nc subvarieties of
the nc unit ball. Given an nc variety $\mathfrak {V} $ in the nc unit ball $\mathfrak {B} _d …

We develop a dilation theory on noncommutative varieties determined by row contractions
T:= T1,..., Tn subject to constraints such as p (T1,..., Tn)= 0, p∈ P, where P is a set of …