Densities on locally compact abelian groups

I. D. Berg; L. A. Rubel

Annales de l'institut Fourier (1969)

  • Volume: 19, Issue: 1, page 81-107
  • ISSN: 0373-0956

Abstract

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A density on a locally compact Abelian group G is a bounded system of compatible measures on the compact quotients of G . We study the Banach algebra of densities on G , using the theory of almost periodic functions as a principal tool. In particular, we characterize those groups G in which each density is induced by a measure on the semi-periodic compactification of G . There are applications to the theory of uniform distribution.

How to cite

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Berg, I. D., and Rubel, L. A.. "Densities on locally compact abelian groups." Annales de l'institut Fourier 19.1 (1969): 81-107. <http://eudml.org/doc/73984>.

@article{Berg1969,
abstract = {A density on a locally compact Abelian group $G$ is a bounded system of compatible measures on the compact quotients of $G$. We study the Banach algebra of densities on $G$, using the theory of almost periodic functions as a principal tool. In particular, we characterize those groups $G$ in which each density is induced by a measure on the semi-periodic compactification of $G$. There are applications to the theory of uniform distribution.},
author = {Berg, I. D., Rubel, L. A.},
journal = {Annales de l'institut Fourier},
keywords = {functional analysis},
language = {eng},
number = {1},
pages = {81-107},
publisher = {Association des Annales de l'Institut Fourier},
title = {Densities on locally compact abelian groups},
url = {http://eudml.org/doc/73984},
volume = {19},
year = {1969},
}

TY - JOUR
AU - Berg, I. D.
AU - Rubel, L. A.
TI - Densities on locally compact abelian groups
JO - Annales de l'institut Fourier
PY - 1969
PB - Association des Annales de l'Institut Fourier
VL - 19
IS - 1
SP - 81
EP - 107
AB - A density on a locally compact Abelian group $G$ is a bounded system of compatible measures on the compact quotients of $G$. We study the Banach algebra of densities on $G$, using the theory of almost periodic functions as a principal tool. In particular, we characterize those groups $G$ in which each density is induced by a measure on the semi-periodic compactification of $G$. There are applications to the theory of uniform distribution.
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/73984
ER -

References

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  1. [1] I.D. BERG, The conjugate space of the space of semi-periodic sequences, Michigan Math. J. 13 (1966), p. 293-297. Zbl0144.16803MR33 #6291
  2. [2] I.D. BERG, M. RAJAGOPALAN and L.A. RUBEL, Uniform distribution on locally compact Abelian groups, Trans. Amer. Math. Soc. 133 (1968) p. 435-446. Zbl0165.34401MR37 #3279
  3. [3] R.C. BUCK, The measure theoretic approach to density, Amer. J. Math. 68 (1946), p. 560-580. Zbl0061.07503MR8,255f
  4. [4] J. CIGLER, Folgen normierter Masse auf kompakten Gruppen, Z. Wahrscheinlichkeitstheorie 1 (1962) p. 3-13. Zbl0109.10702MR26 #7012
  5. [5] E. HEWITT and K.A. ROSS, Abstract Harmonic Analysis, Springer Verlag, Berlin, (1963). Zbl0115.10603
  6. [6] L.A. RUBEL, Uniform distribution in locally compact Abelian groups, Comm. Math. Helv. 93 (1965), p. 253-258. Zbl0152.03703MR31 #3537
  7. [7] W. RUDIN, Fourier Analysis in Groups, Interscience Publishers, (1962), New-York. Zbl0107.09603MR27 #2808

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