Revistes Catalanes amb Accés Obert (RACO)

On approximation and interpolation of entire functions with index-pair $(p,q)$

H. S. Kasana, D. Kumar


In this paper we have studied the Chebyshev and interpolation errors for functions in $\Cal C(E)$, the normed algebra of analytic functions on a compact set $E$ of positive transfinite diameter. The $(p,q)$-order and generalized $(p,q)$-type have been characterized in terms of these approximation errors. Finally, we have obtained a saturation theorem for $f\in\Cal C(E)$ which can be extended to an entire function of $(p,q)$-order 0 or 1 and for entire functions of minimal generalized $(p,q)$-type.

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