Related papers: Positive orthogonal functions
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.
In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions are extremely important for some reasons. First, its…
Let $A$ be a unital $B_{0}$-algebra with an orthogonal basis, then every multiplicative linear functional on $A$ is continuous. This gives an answer to a problem posed by Z. Sawon and Z. Wronski.
This article is a contribution to the spectral theory of so-called eventually positive operators, i.e.\ operators $T$ which may not be positive but whose powers $T^n$ become positive for large enough $n$. While the spectral theory of such…
We consider some multivariate rational functions which have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse…
Due to the exponential increase of the numerical effort with the number of degrees of freedom, moving basis functions have a long history in quantum dynamics. In addition, spawning of new basis functions is routinely applied. Here we…
The goal of this paper is to introduce and study some geometric properties of slice regular functions of quaternion variable like univalence, subordination, starlikeness, convexity and spirallikeness in the unit ball. We prove a number of…
Existence of an increasing quasi-concave value function consistent with given preference information is an important issue in various fields including Economics, Multiple Criteria Decision Making, and Applied Mathematics. In this paper, we…
In this chapter are given necessary and sufficient conditions for the regularity of solutions of the functional equation appearing in the theory of classical orthogonal polynomials. In addition, we also present the functional Rodrigues…
The concept of monogenic functions over real alternative $\ast$-algebras has recently been introduced to unify several classical monogenic (or regular) functions theories in hypercomplex analysis, including quaternionic, octonionic, and…
A version of the recent functional inequality between the Hessians of the square root and the logarithm of positive functions is proven in spaces with non-zero curvature.
In this paper, we study the theory of orthogonal trigonometric polynomials (OTP). We obtain asymptotics of OTP with positive and analytic weight functions by Riemann-Hilbert approach and find they have relations with orthogonal polynomials…
Many new types of sensing or imaging surfaces are based on periodic thin films. It is explained how the response of those surfaces to partially coherent fields can be fully characterized by a set of functions in the wavenumber spectrum…
In this paper we introduce and study a new sequence of positive linear operators acting on function spaces defined on a convex compact subset. Their construction depends on a given Markov operator, a positive real number and a sequence of…
Given a positive weight function and an isometry map on a Hilbert spaces $\mathcal{H}$, we study a class of linear maps which is a $g$-frame, $g$-Riesz basis and a $g$-orthonormal basis for $\mathcal{H}$ with respect to $\mathbb{C}$ in…
In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…
Astrophysical objects frequently exhibit some irregularities or complex behaviour in their light curves. We focus primarily on hot stars, where both radial and non-radial pulsations are observed. One of the primary research goals is to…
A new method of composition orthogonality is introduced. It is applied to generate new sequences of orthogonal polynomials and functions. In particular, classical orthogonal polynomials are interpreted in the sense of composition…
We investigate semiconjugate rational functions, that is rational functions $A,$ $B$ related by the functional equation $A\circ X=X\circ B$, where $X$ is a rational function of degree at least two. We show that if $A$ and $B$ is a pair of…