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Interpolation by Polynomials in z and z-1 on an Annulus

Authors:	BRUTMAN L; VERTESI P; XU Y

Institution:	Department of Mathematics and Computer Science, University of Haifa Haifa 31999, Israel Mathematical Institute of the Hungarian Academy of Sciences H-1053 Budapest, Realtanoda U 13–15, Hungary Department of Mathematics, Temple University Philadelphia, PA 19122, USA

Abstract:	A polynomial of degree n in z^–1 and n–1 in z isdefined by an interpolation projection from the space of functionsanalytic in the annulus r $≤$ \|z\| $≤$ R and continuous on its boundary.The points of interpolation are chosen to coincide with then roots of zⁿ=Rⁿeⁱⁿ (0< ${alpha}$ <2 ${pi}$ /n) and the n roots of zⁿ=rⁿ.The behaviour of the corresponding Lebesgue function is studied,and an estimate for the operator norm is obtained. The resultsof the present paper give a partial affirmative answer to twoconjectures suggested earlier by Mason on the basis of numericalcomputations.

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