ESTIMATES FOR EXPONENTIAL SUMS. APPLICATIONS

摘要

We obtain estimates of exponential (in particular, trigonometric) sums in terms of rational functions. Examples of sharp inequalities are given. These inequalities are used for estimating solutions to linear homogeneous differential equations with constant coefficients. The main results are based on the estimates of the moduli of the derivatives of rational functions by variable majorants (comparison functions) of a special form.