Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article

The support of tempered distributions

  • Colin C. Graham (a1)
Abstract

We identify the support of a tempered distribution by evaluation of a sequence of test functions against the Fourier transform of the distribution. This improves previous results by removing the restriction that the distribution's Fourier transform be in and be of polynomial growth. We use an apparently new technical lemma that implies that certain bounded approximate identities for are also topological approximate identities for elements of the space of Schwartz functions.

Copyright
COPYRIGHT: © Cambridge Philosophical Society 2008
References
Hide All
[1]González Vieli, F. J.Intégrales trigonométriques et pseudofonctions. Ann. Inst. Fourier 44 (1994), 197–211.
[2]González Vieli, F. J.Inversion de Fourier ponctuelle des distributions à support compact. Arch. Math. (Basel) 75 (2000), 290–298.
[3]Vieli, F. J. González. Characterization of the support of pseudomeasures on ℝ. Math. Proc. Camb. Phil. Soc. 135 (2003), 431–442.
[4]González Vieli, F. J. and Graham, C. C.. On the support of tempered distributions. Arch. Math. (Basel) 88 (2007), No. 2, 133–142.
[5]Graham, C. C.. The support of pseudomeasures on ℝ. Math. Proc. Camb. Phil. Soc. 142 (2007), No. 1, 149–152.
[6]Kahane, J.-P. and Salem, R.Ensembles Parfaits et Séries Trigonométriques (Hermann, 1963) (Nouvelle Édition 1994).
[7]Schwartz, L.Théorie des Distributions, II (Hermann, 1951).
[8]Stein, E. M. and Weiss, G.Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, 1971).
[9]Walter, G.Pointwise convergence of distribution expansions. Studia Math. 26 (1966), 143–154.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 59 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×