Related papers: On Certain Positive Semidefinite Matrices of Speci…
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
The purpose of this paper is to investigate the distribution of zeros of entire functions which can be represented as the Fourier transforms of certain admissible kernels. The principal results bring to light the intimate connection between…
This paper discusses further properties of positive partial transpose matrices, with applications towards hyponormal, semi-hyponormal, and $(\alpha,\beta)$-normal matrices. The obtained results present extensions and improvements of many…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
Inspired by certain interesting recent extensions of the gamma, beta and hypergeometric matrix functions, we introduce here new extension of the gamma and beta matrix function. We also introduce new extensions of the Gauss hypergeometric…
Positive definite functions of compact support are widely used for radial basis function approximation as well as for estimation of spatial processes in geostatistics. Several constructions of such functions for ${\mathbb R}^d$ are based…
We define a new class of positive and Lebesgue measurable functions in terms of their asymptotic behavior, which includes the class of regularly varying functions. We also characterize it by transformations, corresponding to generalized…
Given a pair $A,B$ of matrices of size $n\times n$, we consider the matrix function $e^{At+B}$ of the variable $t\in\mathbb{C}$. If the matrix $A$ is Hermitian, the matrix function $e^{At+B}$ is representable as the bilateral Laplace…
Recurrences for positive definite functions in terms of the space dimension have been used in several fields of applications. Such recurrences typically relate to properties of the system of special functions characterizing the geometry of…
We introduce an algorithm to compute the functions belonging to a suitable set ${\mathscr F}$ defined as follows: $f\in {\mathscr F}$ means that $f(s,x)$, $s\in A\subset {\mathbb R}$ being fixed and $x>0$, has a power series expansion…
Several examples of Jacobi matrices with an explicitly solvable spectral problem are worked out in detail. In all discussed cases the spectrum is discrete and coincides with the set of zeros of a special function. Moreover, the components…
Recently, Shehata et al. [37] introduced the $_{r+1}R_{s,k}(B,C,z)$ matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
We give extensions of results on nonnegative matrix semigroups which deduce finiteness or boundedness of such semigroups from the corresponding local properties, e.g., from finiteness or boundedness of values of certain linear functionals…
We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number $r \in \{1\} \cup [2, \infty)$, positive semi-definite matrices $A_i,\…
It is shown that the integrals of the Jacobi polynomials \begin{equation*}%\label{eq:Fn^J} \int_0^t (t-\theta)^\delta P_n^{(\alpha-\frac12,\beta-\frac12)}(\cos \theta) \left(\sin \tfrac{\theta}2\right)^{2 \alpha} \left(\cos…
The property of isotonicity of a continuous convex function defined on the entire space or only on the positive cone is characterized via subdifferentials. Numerous examples illustrating the obtained results are included.
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
We show that any affine invariant function on the set of positive definite matrices must factor through the determinant function, as long as the restriction of the function to scalar matrices is surjective. A motivation from robust…
Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, and satisfy the equation $\Delta f…