Annali di Matematica Pura ed Applicata

, Volume 86, Issue 1, pp 313–324 | Cite as

A strong form of spectral resolution

  • John J. Benedetto


We consider pseudo-measures T on totally disconnected sets E as finitely additive set functions whit the usual variation norm ‖ ‖v. If\(E \subseteq R/2\prod Z\), m(E)=0, T=f′, f ∈L1, and ‖T‖v<∞ then T is a measure. For arbitrary locally compact abelian groups we give conditions that T be a measure in terms of the pseudo-measure norm; this result is known for R/Z.


Abelian Group Variation Norm Strong Form Compact Abelian Group Spectral Resolution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Benedetto,Psendo-Measures and harmonic synthesis, Lecture Notes No. 5, Dept. of Math., U. of Maryland, 1968.Google Scholar
  2. [2]
    J. W. S. Cassels andA. Fröhlich (editors),Algebraic number theory, Thompson Book Co., Washington, D.C., 1967.Google Scholar
  3. [3]
    P. Malliavin,Sur les ensembles ne portant pas de pseudo-measures, C. R. Acad. Sc. Paris, 267 (1968) 813–815.MATHMathSciNetGoogle Scholar
  4. [4]
    W. Rudin,Fourier analysis on groups, J. Wiley and Sons, New York, 1962.Google Scholar
  5. [5]
    N. Varopoulos,Sur les ensembles parfaits et les séries trigonométriques, C. R. Acad. Sc. Paris, 260 (1965) 3831–3834.MATHMathSciNetGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1970

Authors and Affiliations

  • John J. Benedetto
    • 1
  1. 1.U.S.A.

Personalised recommendations