Related papers: Rational inner functions in the Schur-Agler class …
Triangle partition maps form a family that includes many, if not most, well-known multidimensional continued fraction algorithms. This paper begins the exploration of the functional analysis behind the transfer operator of each of these…
We study Clark measures associated with general two-variable rational inner functions (RIFs) on the bidisk, including those with singularities, and with general $d$-variable rational inner functions with no singularities. We give precise…
This paper is a direct continuation of "Functional analysis behind a Family of Multidimensional Continued Fractions: Part I," in which we started the exploration of the functional analysis behind the transfer operators for triangle…
We describe a generalization of the notion of a Hilbert space model of a function in the Schur class of the bidisc. This generalization is well adapted to the investigation of boundary behavior at a mild singularity of the function on the…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to…
A rational function belongs to the Hardy space, $H^2$, of square-summable power series if and only if it is bounded in the complex unit disk. Any such rational function is necessarily analytic in a disk of radius greater than one. The…
In the context of the complex-analytic structure within the unit disk centered at the origin of the complex plane, that was presented in a previous paper, we show that singular Schwartz distributions can be represented within that same…
Using the notions and tools from realization in the sense of systems theory, we establish an explicit and new realization formula for families of infinite products of rational matrix-functions of a single complex variable. Our realizations…
This paper introduces a robust class of functions from finite words to integers that we call Z-polyregular functions. We show that it admits natural characterizations in terms of logics, Z-rational expressions, Z-rational series and…
A rational homogeneous (of degree one) positive real matrix-valued function is presented as the Schur complement of a block of the linear pencil with positive semidefinite matrix coefficients. The partial derivative numerators of a rational…
We study Dirichlet-type spaces $\mathfrak{D}_{\alpha}$ of analytic functions in the unit bidisk and their cyclic elements. These are the functions $f$ for which there exists a sequence $(p_n)_{n=1}^{\infty}$ of polynomials in two variables…
We give a new proof that bounded non-commutative functions on polynomial polyhedra can be represented by a realization formula, a generalization of the transfer function realization formula for bounded analytic functions on the unit disk.
In this article we examine Dirichlet type spaces in the unit polydisc, and multipliers between these spaces. These results extend the corresponding work of G. D. Taylor in the unit disc. In addition, we consider functions on the polydisc…
We prove a realization theorem for rational functions of several complex variables which extends the main theorem of M. Bessmertnyi, "On realizations of rational matrix functions of several complex variables," in Vol. 134 of Oper. Theory…
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…
Polyregular functions are the class of string-to-string functions definable by pebble transducers, an extension of finite-state automata with outputs and multiple two-way reading heads (pebbles) with a stack discipline. If a polyregular…
We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator $S_K$ on a vector-valued Hardy space $H^{2}(\Omega,K)$ is generated by a quasi-inner function, we also provide relationships of…
We study factorizations of operator valued functions of weighted Schur classes over multiply-connected domains. There is a correspondence between functions from weighted Schur classes and so-called ``conservative curved'' systems introduced…
We give a controllable energy-preserving and an observable co-energy-preserving de Branges-Rovnyak functional model realization of an arbitrary given operator Schur function defined on the complex right-half plane. We work the theory out…