On an Inequality for Trigonometric Polynomials In Several Variables

Abstract

This chapter presents trigonometric polynomials in n variables. Using the methods of approximation theory, an inequality can be extended to almost periodic functions and to still more general classes of functions as in the case for Bohr's inequality. However, no analogous result exists in the case of two variables. For the solution of problems containing small divisors, the estimate has to be completed by theorems concerning the best approximation of holomorphic functions by trigonometric polynomials in polystrips. The chapter also presents equations to provide an estimate for a differential operator.