Related papers: Positive and generalized positive real lemma for s…

I show that the projective Schur functions may be interpreted as bispherical functions of either the triple (q(n),gl(n,n),q(n)), where q(n) is the "odd" (queer) analog of the general liner Lie algebra, or the triple (p(n),gl(n,n),p(n)),…

In this paper, by the generalized Bell umbra and Rolle's theorem, we give some results on the real rootedness of polynomials. Some applications on partition polynomials and the sigma polynomials of graphs are given.

Many well-known positive linear operators (like Bernstein, Baskakov, Sz\'{a}sz-Mirakjan) are constructed by using specific fundamental functions. The sums of the squared fundamental functions have been objects of study in some recent…

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…

The main goal of this work is classifying the singularities of slice regular functions over a real alternative *-algebra A. This function theory has been introduced in 2011 as a higher-dimensional generalization of the classical theory of…

We study properties of inner and outer functions in the Hardy space of the quaternionic unit ball. In particular, we give sufficient conditions as well as necessary ones for functions to be inner or outer.

We consider and provide an accurate study for the fractional Zernike functions on the punctured unit disc, generalizing the classical Zernike polynomials and their associated $\beta$-restricted Zernike functions. Mainly, we give the…

The aim of this paper is to prove that a large class of quaternionic slice regular functions result to be (ramified) covering maps. By means of the topological implications of this fact and by providing further topological structures, we…

We consider polynomials on the intersection of the closed positive orthant with the height-$1$ level hypersurface of certain polynomials with positive coefficients. We show that any polynomial strictly positive on such a semi-algebraic set…

We study the space, $R_m$, of $m$-symmetric functions consisting of polynomials that are symmetric in the variables $x_{m+1},x_{m+2},x_{m+3},\dots$ but have no special symmetry in the variables $x_1,\dots,x_m$. We obtain $m$-symmetric…

The primary objective of this paper is to establish an algebraic framework for the space of weakly slice regular functions over several quaternionic variables. We recently introduced a $*$-product that maintains the path-slice property…

We prove the Plancherel formula for hypergeometric functions associated to a root system in the situation when the root multiplicities are negative (but close to 0). As a result we obtain a classification of the hypergeometric functions…

We characterize a holomorphic positive definite function $f$ defined on a horizontal strip of the complex plane as the Fourier-Laplace transform of a unique exponentially finite measure on $\mathbb{R}$. The classical theorems of Bochner on…

In this paper, we are concerned with the S-polyregularity the regular dot product of slice regular functions. We prove that the product of a slice regular function and right quaternionic polynomial function is a S-polyregular function and…

We study a linear map on symmetric functions that ``divides'' a partition by a positive integer $k$, sending a Schur function indexed by a partition of $kn$ to a symmetric function indexed by partitions of $n$. We determine its Schur…

A real seminormed involutive algebra is a real associative algebra ${\mathcal A}$ endowed with an involutive antiautomorphism $*$ and a submultiplicative seminorm $p$ with $p(a^*) =p(a)$ for $a\in {\mathcal A}$. Then ${\mathop{\tt…

This note characterizes multiplicative linear functionals on reproducing kernel Hilbert spaces of functions on the Euclidean unit ball in complex d-dimensional space, in terms of their action on kernel functions. The kernels considered are…

This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises…

In this paper, we determine the partial positivity(resp., negativity) of the curvature of all irreducible Riemannian symmetric spaces. From the classifications of abstract root systems and maximal subsystems, we can give the calculations…

We study the vanishing sets of slice regular polynomials in several quaternionic variables. We obtain a geometric description of the vanishing sets in two variables, which leads to a new version of the Strong Hilbert Nullstellensatz in the…