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A baire approach to quantitative resonance principles |
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| Authors: | E. van Wickeren |
| Affiliation: | Lehrstuhl A für Mathematik Rheinisch-Westf?lische Technische Hochschule Aachen , Templergraben 55, Aachen, D-5100, Germany |
| 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. |
| Keywords: | Peano kernel theorem mass theorem quotient theorem Sard's factorisation theorem open mapping theorem representation of linear functionals functions of (normalised) bounded variation Riemann-Stieltjes measure integration by parts moment (orthogonality) condition Sobolev space interpolation quadrature B-spline Primary 41A65 Primary 41A80 Primary 46E15 Secondary 26A06 Secondary 41A05 Secondary 41A10 Secondary 41A55 Secondary 65J05 |