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We define -polynomials as linear combinations of dilations by some frequencies of an entire function . In this paper, we use Padé interpolation of holomorphic functions in the unit disk by -polynomials to obtain explicitly approximating -polynomials with sharp estimates on their coefficients. We show that when frequencies lie in a compact set ⊂ℂ, then optimal choices for the frequencies of interpolating -polynomials are similar to Fekete points. Moreover, the minimal norms of the interpolating operators form a sequence whose rate of growth is determined by the transfinite diameter of .In case of the Laplace transforms of measures on , we show that the coefficients of interpolating -polynomials stay bounded provided that the frequencies are Fekete points. Finally, we give a sufficient condition for measures on the unit circle that ensures that the sums of the absolute values of the coefficients of interpolating -polynomials stay bounded.

Padé Interpolation by F-Polynomials and Transfinite Diameter