[en] This paper discusses methods and software for C¹ interpolation at arbitrarily distributed data points in the plane. The primary results presented here are derivative-estimation procedures which lead to interpolatory surfaces constituting very accurate approximations for a variety of test functions

[en] In this paper we derive a formula for the rank of the self-commutator of hyponormal block Toeplitz operators T_Φ with matrix-valued rational symbols Φ in L^∞(C^nxn) via the classical Hermite-Fejer interpolation problem

[en] The discrete Fourier calculus of the four families of special functions, called C–, S–, S^s– and S^l -functions, is summarized. Functions from each of the four families of special functions are discretely orthogonal over a certain finite set of points. The generalizations of discrete cosine and sine transforms of one variable — the discrete S^s– and S^l-transforms of the group F₄ — are considered in detail required for their exploitation in discrete Fourier spectral methods. The continuous interpolations, induced by the discrete expansions, are presented

[en] Non-relativistic potential models are considered of the pure power V(r)sgn(q)r^q and logarithmic V(r)=ln(r) types. It is shown that, from the spectral viewpoint, these potentials are actually in a single family. The log spectra can be obtained from the power spectra by the limit q→0 taken in a smooth representation P_nl(q) for the eigenvalues E_nl(q). A simple approximation formula is developed which yields the first 30 eigenvalues with an error less than 0.04%. (author)

[en] Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no simple explanation of this phenomenon is known. We show that, in the case of von Neumann measurements, the ability to interpolate measurements is an operational principle that sets apart LOCC and separable operations

[en] In this paper we apply the concept of difference relation to the sequences of k–Fibonacci numbers. We will obtain general formulas to find any term of the ith k–Fibonacci difference sequence from the initial k–Fibonacci numbers. We also find formulas for the sum of the elements of these new sequences as well as their generating functions. Finally, we study the k–Fibonacci Newton polynomial interpolation.

[en] The rationale for the polynomial root interpolation method is presented. The formulation of interpolators and their properties are given. A summary of surfaces fit by these interpolators is included. As an example, the appli- cation of the fitting procedure to a potential energy surface for the ground electronic state of water is calculated by the CNDO/2 method. Interpolation by polynomial roots shows promise, but has not yet been demonstrated to be a viable procedure. The problems still to be addressed are listed

No abstract available

[en] In this paper we use new function spaces and interpolation methods to study the dependence of the properties of summable multiple Fourier series on their coefficients. We obtain theorems for multiple orthogonal series that reinforce the Hardy-Littlewood theorem for trigonometric series. We prove inequalities of Hardy-Littlewood-Paley type for multiple orthogonal series that refine certain well-known inequalities of this kind

[en] The paper deals with the problem of extremal interpolation in the mean for large averaging intervals with the minimal value of the norm of a linear differential operator with constant real coefficients in the case when the extremal functions are L-splines