Related papers: Inner-outer factorization of analytic matrix-value…
We continue studying the problem of analytic approximation of matrix functions. We introduce the notion of a partial canonical factorization of a badly approximable matrix function $\Phi$ and the notion of a canonical factorization of a…
We obtain a general characterization of discrete-time all-pass rational matrix functions from state-space representations. It can be employed to address model reduction problems in the same vein of the theory developed by Glover in the…
This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by the geometric mean of the condition number and the dimension…
Prime factorization is an outstanding problem in arithmetic, with important consequences in a variety of fields, most notably cryptography. Here we employ the intriguing analogy between prime factorization and optical interferometry in…
In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, $n$ variables, the four field operations and radical extractions). We…
A previously established correspondence between definite-parity real functions and inner analytic functions is generalized to real functions without definite parity properties. The set of inner analytic functions that corresponds to the set…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
We construct operators which factorize the transfer function associated with a non-self-adjoint 2x2 operator matrix whose diagonal entries can have overlapping spectra and whose off-diagonal entries are unbounded operators.
Multivariable, real-valued functions induce matrix-valued functions defined on the space of d-tuples of n-times-n pairwise-commuting self-adjoint matrices. We examine the geometry of this space of matrices and conclude that the best notion…
Positive-definite matrices materialize as state transition matrices of linear time-invariant gradient flows, and the composition of such materializes as the state transition after successive steps where the driving potential is suitably…
Let $H^{\infty}(E)$ be a non commutative Hardy algebra, associated with a $W^*$-correspondence $E$. In this paper we construct factorizations of inner-outer type of the elements of $H^{\infty}(E)$ represented via the induced representation,…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
In this paper we prove a few propositions concerning factorizations of morphisms in pro categories, the most important of which solves an open problem of Isaksen concerning the existence of certain types of functorial factorizations. On our…
This is the second of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
We examine factorisation in the connected prescription of Yang-Mills amplitudes. The multi-particle pole is interpreted as coming from representing delta functions as meromorphic functions. However, a naive evaluation does not give a…
We give a complete description of outer functions in the analytic weighted Lipschitz algebras by their moduli in the boundary, with respect to any modulus of continuity.
The algebraic structure of V.P. Potapov's Fundamental Matrix Inequality (FMI) is discussed and its interpolation meaning is analyzed. Functional model spaces are involved. A general Abstract Interpolation Problem is formulated which seems…
This paper considers the factorization of elliptic symbols which can be represented by matrix-valued functions. Our starting point is a \textit{Fundamental Factorization Theorem}, due to Budjanu and Gohberg. We critically examine the work…
We present a motivating example for matrix multiplication based on factoring a data matrix. Traditionally, matrix multiplication is motivated by applications in physics: composing rigid transformations, scaling, sheering, etc. We present an…