Related papers: Characteristic function of M. Liv\v{s}ic and some …
The first three results in this thesis are motivated by a far-reaching conjecture on boundedness of singular Brascamp-Lieb forms. Firstly, we improve over the trivial estimate for their truncations, thus excluding potential trivial…
The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.
On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…
In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…
Neat stuff about eigenfunctions, transfer matrices, and a.c. spectrum of one-dimensional Schrodinger operators
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
The results on the inversion of convolution operators and Toeplitz matrices in the 1-D (one dimensional) case are classical and have numerous applications. We consider a 2-D case of Toeplitz-block Toeplitz matrices, describe a minimal…
Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea…
When lattice QCD is formulated in sectors of fixed quark numbers, the canonical fermion determinants can be expressed explicitly in terms of transfer matrices. This in turn provides a complete factorization of the fermion determinants in…
The Cayley-Hamilton problem of expressing functions of matrices in terms of only their eigenvalues is well-known to simplify to finding the inverse of the confluent Vandermonde matrix. Here, we give a highly compact formula for the inverse…
We introduce the notion of characteristic function of a quaternionic matrix, whose roots are the left eigenvalues. We prove that for all $2\times 2$ matrices and for $3\times 3$ matrices having some zero entry outside the diagonal there is…
We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input-plant-output systems to arbitrary quantum nonlinear Markovian input-output models. This is intended as a tool in the…
We study various convex functions on $R^n$ associated with positive definite matrices. This yiels some exotic Holder matrix inequalities.
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
It is common in functional data analysis to look at a set of related functions: a set of learning curves, a set of brain signals, a set of spatial maps, etc. One way to express relatedness is through an additive model, whereby each…
In this paper, we introduce a new generalized class of analytic functions involving the Mittag-Leffler operator and Bazilevi\u{c} functions. We examine inclusion properties, radius problems and an application of the generalized…
We review how some multianalytic inner functions of the Beurling type theorem are associated to row contractions following works of G.Popescu. Motivated by a result on weak Markov dilations, we define a notion of characteristic function for…
Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…
Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…
We introduce conservative curved systems over multiply connected domains and study relationships of such systems with related notions of functional model, characteristic function, and transfer function. In contrast to standard theory for…