Related papers: Inner functions and operator theory
This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and…
For a topological space it is well-known that the associated closure and interior operators provide equivalent descriptions of set-theoretic topology; but it is not generally true in other categories, consequently it makes sense to define…
We prove a Hankel-variant commutant lifting theorem. This also uncovers the complete structure of the Beurling-type reducing and invariant subspaces of Hankel operators. Kernel spaces of Hankel operators play a key role in the analysis.
We study Toeplitz operators with respect to a commuting $n$-tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a particular such tuple on a function space. The algebra of…
In this paper, to solve the invariant subspace problem, contraction operators are classified into three classes ; (Case 1) completely non-unitary contractions with a non-trivial algebraic element, (Case 2) completely non-unitary…
The main aim of this book is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator…
We study the relations between maximal functions in a Toeplitz kernel and those in a subkernel of the same Toeplitz operator, as well as the question of how multipliers between Toeplitz kernels act on subkernels. We use those relations to…
Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two folded: (i) we provide a set…
We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on a Hilbert space. As applications, we characterize compactness of affine and Weyl-Heisenberg localization operators as well as…
By a famous result, functions in backward shift invariant subspaces in Hardy spaces are characterized by the fact that they admit a pseudocontinuation a.e. on $\T$. More can be said if the spectrum of the associated inner function has holes…
The paper contains a survey of the results obtained during the last ten years in the theory of elliptic boundary problems in H\"ormander function spaces, developed by the authors, and other related results of modern analysis. The basics of…
We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
Operator monotone functions, introduced by Lowner in 1934, are an important class of real-valued functions. They arise naturally in matrix and operator theory and have various applications in other branches of mathematics and related…
We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in $R^d$. As the most traditional definition of Toeplitz operators via Bergman-type projection is not available here, we use an approach…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
This is a survey paper. We discuss Toeplitz operators in K\"ahler geometry, with applications to geometric quantization, and review some recent developments.
We give a characterization of the compact operators on a model space in terms of asymptotic Toeplitz operators.
The spectral metric and Einstein functionals defined by two vector fields and Laplace-type operators over vector bundles, giving an interesting example of the spinor connection and square of the Dirac operator. Motivated by the spectral…