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On deviations from rational functions of entire functions of finite lower order

E. Ciechanowicz, I. I. Marchenko (2007)

Annales Polonici Mathematici

Let f be a transcendental entire function of finite lower order, and let q ν be rational functions. For 0 < γ < ∞ let B(γ):= πγ/sinπγ if γ ≤ 0.5, B(γ):= πγ if γ > 0.5. We estimate the upper and lower logarithmic density of the set r : 1 ν k l o g m a x | | z | | = r | f ( z ) q ν ( z ) | 1 < B ( γ ) T ( r , f ) .

On discrepancy theorems with applications to approximation theory

Hans-Peter Blatt (1995)

Banach Center Publications

We give an overview on discrepancy theorems based on bounds of the logarithmic potential of signed measures. The results generalize well-known results of P. Erdős and P. Turán on the distribution of zeros of polynomials. Besides of new estimates for the zeros of orthogonal polynomials, we give further applications to approximation theory concerning the distribution of Fekete points, extreme points and zeros of polynomials of best uniform approximation.

On Dittmar's approach to the Beltrami equation

Ewa Ligocka (2002)

Colloquium Mathematicae

We recall an old result of B. Dittmar. This result permits us to obtain an existence theorem for the Beltrami equation and some other results as a direct consequence of Moser's classical estimates for elliptic operators.

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