Related papers: Functional Models and Minimal Contractive Liftings
The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators…
We prove that functions with compact support in non-quasianalytic classes of Roumieu-type and of Beurling-type defined by a weight matrix with some mild regularity conditions can be characterized by the decay properties of their Fourier…
We discuss the classes $\fC$, $\fM$, and $\fS$ of analytic functions that can be realized as the Liv\v{s}ic characteristic functions of a symmetric densely defined operator $\dot A$ with deficiency indices $(1,1)$, the Weyl-Titchmarsh…
It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal…
This paper is dedicated to the introduction in a circle of ideas and methods, which are connected with the notion of characteristic function of a non-selfadjoint operator. We start with the consideration of closed and open systems…
Passive discrete-time systems in Pontryagin space setting are investigated. In this case the transfer functions of passive systems, or characteristic functions of contractive operator colligations, are generalized Schur functions. The…
We introduce a formal operational semantics that describes the fused execution of variable contraction problems, which compute indexed arithmetic over a semiring and generalize sparse and dense tensor algebra, relational algebra, and graph…
For a functor $Q$ from a category $C$ to the category $Pos$ of ordered sets and order-preserving functions, we study liftings of various kind of structures from the base category $C$ to the total(or Grothendieck) category $\int Q$. That…
We introduce a nonlinear aggregation type classifier for functional data defined on a separable and complete metric space. The new rule is built up from a collection of $M$ arbitrary training classifiers. If the classifiers are consistent,…
Truncated Toeplitz operators are compressions of multiplication operators on $L^2$ to model spaces (that is, subspaces of $H^2$ which are invariant with respect to the backward shift). For this class of operators we prove certain Szeg\"o…
In categorical realizability, it is common to construct categories of assemblies and categories of modest sets from applicative structures. These categories have structures corresponding to the structures of applicative structures. In the…
We extend Agler's notion of a function algebra defined in terms of test functions to include products, in analogy with the practice in real algebraic geometry, and hence the term preordering in the title. This is done over abstract sets and…
We compute exactly various 4-point correlation functions of shortest scalar operators in bi-scalar planar four-dimensional "fishnet" CFT. We apply the OPE to extract from these functions the exact expressions for the scaling dimensions and…
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
In this article, we construct operator models for meromorphic functions of bounded type on Krein spaces. This construction is based on certain reproducing kernel Hilbert spaces which are closely related to model spaces. Specifically, we…
We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Moebius group of the projective line. Since the general proof is very simple but not…
We present a solution of the operator-valued Schur-function realization problem on the right-half plane by developing the corresponding de Branges-Rovnyak canonical conservative simple functional model. This model corresponds to the closely…
The motivation behind this paper is threefold. Firstly, to study, characterize and realize operator concavity along with its applications to operator monotonicity of free functions on operator domains that are not assumed to be matrix…
Classical functional calculus is primarily spectral, capturing eigenvalue information through resolvent methods while largely ignoring nilpotent structure. Building on the projector-nilpotent characterization developed in our companion…
This paper shows that an analytic space $X$ has a unique maximal model through which every proper surjective morphism from a non-singular analytic space to $X$ factors. This is called the {\sl geometric minimal model} of $X$ and…