A baire approach to quantitative resonance principles

Abstract

The main purpose of this paper is to give a proof of quantitative resonance and condensation principles via Baire category arguments in contrast to the gliding hump method used previously. Thereby a new nonquantitative resonance principle is established which is concerned with dominated convergence in Frechet spaces, by the way yielding more detailed information on the structure of the underlying spaces. On the other hand, Baire's approach is an easy tool to develop condensation principles by considering residual sets. Finally, some typical applications concerning trigonometric Fourier partial sums may illustrate the result received.