Herglotz's representation of holomorphic functions with positive real part and Carathéodory's
theorem on approximation by inner functions are two well‐known classical results in the …

(4) There is a one-to-one correspondence between operator-valued contractive holomorphic
functions and canonical model triples. This pertains to the new realization formula …

We study the pairs of commuting contractions that are annihilated by polynomials with a
geometric condition on its zero set, herein called the toral algebraic pairs. Toral algebraic …

A bounded Hilbert space operator $ T $ for which the closure of an annulus\[\mathbb {A}
_r=\{z\:\r<| z|< 1\}\subseteq\mathbb {C}\\\\(0< r< 1)\] is a spectral set is called an $\mathbb {A} …

In this article we solve four special cases of the truncated Hamburger moment problem
(THMP) of degree 2 k with one or two missing moments in the sequence. As corollaries we …

The pentablock, denoted as P, is defined as follows: P={(a 21, tr (A), det (A)): A=[aij] 2× 2
with‖ A‖< 1}. It originated from the work of Agler–Lykova–Young in connection with a …

The Herglotz representation theorem for holomorphic functions with non-negative real part is
a fundamental result in the theory of holomorphic functions. In this paper, we reinterpret the …

A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator T can be
dilated to a unitary U, ie, T n= PHU n| H for all n= 0, 1, 2,…. A more general multivariable …

A commuting tuple of Hilbert space operators $(T_1,\dotsc, T_n) $ is said to be an\textit
{$\mathbb {A} _r^ n $-contraction} if the closure of the polyannulus\[\mathbb A_r …

The Herglotz representation of holomorphic functions with positive real part and
Carath\'eodory's theorem on approximation by inner functions are two well-known classical …