[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)

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[en] We construct an explicit formula for the fractal interpolation function associated to an IFS with variable parameters. The solution is given in terms of the base p representation of numbers. This construction is a consequence of the formulation of the problem in a general functional equation setting. We introduce compatibility conditions as essential hypotheses to ensure problems in the functional system form are well-defined

[en] A procedure for presenting tabular data, such as are contained in the ENDF/B files, that is simpler, more general, and potentially much more compact than the present schemes used with ENDF/B is presented. The method has been successfully used for Bondarenko interpolation in a module of the AMPX system. 1 figure, 1 table

[en] Critical remarks are made concerning mass tables in general and the mass table based on mass relationships in particular. Specific criteria for acceptability of a table are formulated. Two methods--which form a logical sequence--of using these relationships to predict masses are described. The first involves the construction of regional mass tables with a very limited number of free parameters to be adjusted. The second involves the prediction of each unknown mass individually and independently and uses no parameters whatsoever

[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