## On weighted lacunary interpolation

Margit Lénárd

### Abstract

In this paper the regularity of a special lacunary interpolation problem is investigated, where for a given $r$ ($r\geq 2$, $r\in {\bf N})$ the derivatives up to the $r$-2nd order together with the weighted $r$th derivative are prescribed at the nodes. Sufficient conditions on the nodes and the weight function, for the problem to be regular, are derived. Under these conditions a method to construct the explicit formulae for the fundamental polynomials of the regular weighted lacunary interpolation is discussed. Examples are presented using the roots of the classical orthogonal polynomials.

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### Key words

Birkhoff interpolation, lacunary interpolation, Hermite interpolation, weighted $(0,2)$-interpolation, weighted $(0,1,3)$-interpolation, regularity, explicit formulae

41A05

### Links to the cited ETNA articles

 [4] Vol. 25 (2006), pp. 206-223 Margit Lénárd: On weighted (0,2)-type interpolation

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