We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for the functionals. This shows that the vanishing of the tau-function for those systems is the obstruction to the solvability of a Riemann–Hilbert problem asso...

in this study a numerical method is developed to solve the hammerstein integral equations. to this end the kernel has been approximated using the leastsquares approximation schemes based on legender-bernstein basis. the legender polynomials are orthogonal and these properties improve the accuracy of the approximations. also the nonlinear unknown function has been approximated by using the berns...

Orthogonal zero interpolants (OZI) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. OZI’s can be constructed by the 3-term recurrence relation. These interpolants are found useful in the solution of constrained approximation problems and in the structure of Gauss-type quadrature rules. We present some theoretical...

Using Casorati determinants of Charlier polynomials (ca n )n , we construct for each finite set F of positive integers a sequence of polynomials cF n , n ∈ σF , which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF ( N. For suitable finite sets F (we call them admissible sets), we prove that the polynomials cF n , n ∈ σF , a...

Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets centers that are not determining for polynomials. It shown polynomial consistence sufficient in order to define kernel-based numerical the functional usual properties optimal recovery. Application examples include generation sparse differentiation formulas Laplacian a grid accurate ...

Let L be a quasi-definite linear functional defined on the linear space of polynomials with real coefficients. In the literature, three canonical transformations of this functional are studied: xL, L + Cδ(x) and x L + Cδ(x) where δ(x) denotes the linear functional (δ(x))(xk) = δk,0, and δk,0 is the Kronecker symbol. Let us consider the sequence of monic polynomials orthogonal with respect to L....

In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural genera...