Evgeny Poletsky
Padé interpolation by $F$-polynomials and transfinite diameter
We define $F$-polynomials as linear combinations of dilations of an entire functions $F$. We use Padé interpolation by $F$-polynomials to obtain explicitly approximating $F$-polynomials
with estimates for their coefficients. We show that when frequencies lies in a compact set $K$ in the complex plane then optimal choices for the frequencies of interpolating polynomials are similar to Fekete points and the minimal norms of the interpolating operators form a sequence
whose rate of growth is determined by the transfinite diameter.
For the Laplace transforms of measures on $K$ we show that the coefficients of interpolating polynomials stay bounded provided the frequencies are Fekete points. Finally, we give sufficient condition for measures on the unit circle so that the sums of the absolute values
of the coefficients of interpolating polynomials stay bounded.
This is joint work with Dan Coman.