Related papers: Positive orthogonal functions
Carath\'eodory functions, i.e. functions analytic in the open upper half-plane and with a positive real part there, play an important role in operator theory, $1D$ system theory and in the study of de Branges-Rovnyak spaces. The Herglotz…
Functions whose symmetries form a crystallographic group in particular have a lattice of periods, and the set of their level curves forms a periodic pattern. We show how after projecting these functions, one obtains new functions with a…
Positive definite functions are fundamental to many areas of applied mathematics, probability theory, spatial statistics and machine learning, amogst others. Motivated by a problem coming from the maximum likelihood estimation under fixed…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…
In this survey article, we review some results and conjectures related to orthogonal polynomials on Cantor sets. The main purpose of this paper is to emphasize the role of equilibrium measures in order to have a general theory of…
In this paper the spherical quasi-convexity of quadratic functions on spherically convex sets is studied. Several conditions characterizing the spherical quasi-convexity of quadratic functions are presented. In particular, conditions…
Based on the results about the invariant cones appeared in the literature this paper analyses the existence of periodic orbits in three-dimensional continuous piecewise linear homogeneous systems with two zones, and a necessary and…
System of alternatively orthogonalized rational functions of Jacobi type on the half line $[1, \infty)$ is defined and its properties are established. Three subsystems of proper and mixed systems of rational functions with nice properties…
For linear bose field theories, I show that if a classical Hamiltonian function is strictly positive, then there is a canonical transformation making the evolution orthogonal. This structure theorem is used to analyze the corresponding…
We give a local characterization of the class of functions having positive distributional derivative with respect to $\bar{z}$ that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild non-degeneracy…
The article describes a topological theory of quasiperiodic functions on the plane. The development of this theory was started (in different terminology) by the Moscow topology group in early 1980s. It was motivated by the needs of solid…
Orthogonal Graph Representations are essential tools for testing existence of hidden variables in quantum theory. As required by the interpretation of Copenhaghe on the foundations of quantum mechanics, a physical observable is not…
We consider one-dimensional systems in the presence of a quasi-periodic perturbation, in the analytical setting, and study the problem of existence of quasi-periodic solutions which are resonant with the frequency vector of the…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
We construct an orthogonal basis of functions defined over the unit circle as the product of the common sinusoidal functions of the azimuth angle by radial functions which are essentially sines of a polynomials of the radial distance to the…
The notion \emph{Perron-Frobenius theory} usually refers to the interaction between three properties of operator semigroups: positivity, spectrum and long-time behaviour. These interactions gives rise to a profound theory with plenty of…
Due to the fundamental works of T. Ando, W. Szyma\'nski, F. H. Szafraniec, and many others it is well known that sesquilinear forms play an important role in dilation theory. The crucial fact is that every positive definite operator…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…