Related papers: Moment Problems and Spectral Functions
We introduce the notion of a \lambda-nonisotropically balanced domain and show that the symmetrized polydisc in C^n, n \geq 2, is an example of such a domain. Given a \lambda-nonisotropically balanced domain \Omega, we derive effective…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting…
We prove a factorization theorem for reproducing kernel Hilbert spaces whose kernel has a normalized complete Nevanlinna-Pick factor. This result relates the functions in the original space to pointwise multipliers determined by the…
We study interpolation L-systems realizing finite Nevanlinna-Pick data sets and analyze their structural and quantitative characteristics. Explicit formulas are derived for the c-entropy and dissipation coefficient, two intrinsic invariants…
We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach…
In this paper we formulate and solve Nevanlinna-Pick and Carath\'eodory type problems for tensor algebras with data given on the N-dimensional operator unit ball of a Hilbert space. We develop an approach based on the displacement structure…
The synthesis of optimization algorithms typically follows a design-first-analyze-later approach, which often obscures fundamental performance limitations and hinders the systematic design of algorithms operating at the achievable…
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
We provide an effective single-matrix criterion, in terms of what we call the elementary Pick matrix, for the solvability of the noncommutative Nevanlinna-Pick interpolation problem in the row ball, and provide some applications. In…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
The derivation of dynamical laws for general observables (or moments) from the master equation for the probability distribution remains a challenging problem in statistical physics. Here, we present an alternative formulation of the general…
The problem of existence of solutions to nabla differential equations and nabla differential inclusions on time scales is considered. Under a special form of the set-valued constraint map, sufficient conditions for the existence of at least…
In the paper `Distinguished Varieties,' Agler and McCarthy used Hilbert function spaces to study the uniqueness properties of the Nevanlinna-Pick problem on the bidisc. In this work we give a geometric procedure for constructing a…
We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data…
Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…
Several recent imaging experiments access the equilibrium density profiles of interacting particles confined to a two-dimensional substrate. When these particles are in a fluid phase, we show that such data yields precise information…
Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…
We introduce a "dual-space approach" to mixed Nevanlinna-Pick/Carath\'eodory-Schur interpolation in Banach spaces X of holomorphic functions on the disk. Our approach can be viewed as complementary to the well-known commutant lifting…
We prove the convergence of an incremental projection numerical scheme for the time-dependent incompressible Navier--Stokes equations, without any regularity assumption on the weak solution. The velocity and the pressure are discretised in…