Recently SHARMA, SMITH and TZIMBALARIO [11] have given the necessary and sufficient condition when the problem of (0, m~ . . . . , mg) interpolation by trigono2kn metric polynomials on the nodes (k--0, 1 . . . . . n l ) is uniquely solvable n (or regular) where m~, ms . . . . , mq are given positive integers. A different proof of this result was given earlier by CAVARETTA, SHARMA and VAROA [1]. In order to state the result precisely we shall consider trigonometric polynomials of the class oq M and ~M,, (e=0 or 1). We shall say that T(O) E~'u if

Convergence of lacunary trigonometric interpolation on equidistant nodes

Following four important papers on Birkhoff interpolation by Turan and his associates ([2], [3], [4], [14]), Kis ([8], [19]) proved the following theorems.

/pdf/hermite-birkhoff-trigonometric-interpolation-in-the-0-1-2-m-2l8t781eqx.pdf

Hermite-Birkhoff trigonometric interpolation in the (0, 1, 2, M) case

Equiconvergence of some Lacunary trigonometric interpolation polynomials

In this paper we give sufficient conditions (Theorem 1) for the existence and uniqueness of solutions of certain boundary value problems for an nth order linear ordinary differential on a compact interval l of the reals Sufficient conditions (Theorem 2) are also given for the existence of certain zero multipoint boundary value problems for an nth order nonlinear differential equation

Interpolation in the Solution Sets of Ordinary Differential Equations

In an earlier work [12] we considered the case of (0, 2, 3) interpolation by trigonometric polynomials at the points , i = 0, 1,…, n-1. By (0, 2, 3) interpolation we mean the problem of finding a trigonometric polynomial of suitable order whose values, second and third derivatives are prescribed at some given points. An interesting distinction between the (0, 2) interpolation studied by the Hungarian mathematician O.

An application of a theorem of J. Czipszer and G. Freud to a problem of simultaneous approximation

/pdf/trigonometric-interpolation-0-2-3-case-1zt95ucw20.pdf

Trigonometric interpolation (0, 2, 3) case

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Trigonometric interpolation (0, 2, 3) case