We define F-polynomials as linear combinations of dilations by some
frequencies of an entire function F. In this paper we use Pade interpolation
of holomorphic functions in the unit disk by F-polynomials to obtain
explicitly approximating F-polynomials with sharp estimates on their
coefficients. We show that when frequencies lie in a compact set
KβC 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 K.
In case of the Laplace transforms of measures on K, 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 which ensures that the sums of the absolute values
of the coefficients of interpolating polynomials stay bounded.Comment: 16 page