Function spaces inclusions and rate of convergence of Riemann-type sums in numerical integration

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In signal processing, discrete convolutions are usually involved in fast calculating coefficients of time-frequency decompositions like wavelet and Gabor frames. Depending on the regularity of the mother analyzing functions, one wants to detect the right resolution in order to achieve good approximations of coefficients. Local-global conditions on functions in order to get the convergence rate of Riemann-type sums to their scalar products in L2 are presented. Wiener amalgam spaces, in particular W(C0,l2) for the space-time domain and W(L2,l1) for the frequency domain, give natural norms in order to estimate errors. In particular, relations between the rate of convergence of these series to integrals by increasing resolution and the (minimal) required Besov regularity are presented by means of functional and harmonic analysis techniques.

Original languageEnglish
Pages (from-to)45-57
Number of pages13
JournalNumerical Functional Analysis and Optimization
Volume24
Issue number1-2
DOIs
StatePublished - 2003
Externally publishedYes

Keywords

  • Decomposition spaces
  • Discrete convolutions
  • Function spaces inclusions
  • Sampling theory
  • Wavelets

Fingerprint

Dive into the research topics of 'Function spaces inclusions and rate of convergence of Riemann-type sums in numerical integration'. Together they form a unique fingerprint.

Cite this