Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Invariant subspaces of the maximal domain
of the Fourier transform


Authors: Gilbert Muraz and Pawel Szeptycki
Journal: Proc. Amer. Math. Soc. 125 (1997), 3275-3278
MSC (1991): Primary 42A38, 43A30
DOI: https://doi.org/10.1090/S0002-9939-97-03973-7
MathSciNet review: 1402877
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Translation invariant subspaces of the maximal domain of the Fourier transform (the amalgam of $l^2$ with $L^1$) are characterised: it turns out that in this case all measurable subsets of the dual space are sets of spectral synthesis.


References [Enhancements On Off] (What's this?)

  • [AS] N. Aronszajn, P.Szeptycki, On General Integral Transformations, Math. Annalen 163 (1966) 127-154MR 32:8209
  • [BD] F. P. Bertrandias, C. Dupuis, Analyse harmonique sur les espaces $l^p(L^{p'})$, Ann. Inst. Fourier XXIX (1979), 189-206.
  • [E] R.E. Edwards, Fourier Series, vol. II, Holt, Rinehart and Winston, 1967MR 36:5588
  • [FS] John J. F. Fournier, J. Stewart, Amalgams of $L^p$ and $l^q$, Bull A.M.S., 13 (1985) 1-21MR 86f:46027
  • [G] Emilo Gagliardo, On integral transformations with positive kernels, Proceedings AMS, 16, (1965), 429-434
  • [K] Yitzhak Katznelson, An introduction to Harmonic Analysis, John Wiley and Sons, Inc. 1968 MR 40:1734
  • [O] A. Olevskii, Translation invariant complemented subspaces in $L^p(\mathbb {R})$, Real Analysis Exchange 21 (1995/96), 16-17.
  • [S1] P. Szeptycki, On functions and measures whose Fourier transforms are functions, Math. Ann. 179 (1968) 31-41 MR 39:710
  • [S2] P. Szeptycki, On some problems related to the extended domain of Fourier transform, Rocky Mountain J. of Math.,10 (1980) 99-103MR 82a:42012

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42A38, 43A30

Retrieve articles in all journals with MSC (1991): 42A38, 43A30


Additional Information

Gilbert Muraz
Affiliation: Department of Mathematics, Institut Fourier–Grenoble, UFR-UMR 5582, BP 74, 38402 St. Martin d’Heres Cedex, France
Email: muraz@fourier.ujf-grenoble.fr

Pawel Szeptycki
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: szeptycki@kuhub.cc.ukans.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03973-7
Keywords: Fourier transform, maximal domain
Received by editor(s): August 29, 1995
Received by editor(s) in revised form: May 20, 1996
Additional Notes: Supported in part by the General Research Fund, University of Kansas
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society