# Densities on locally compact abelian groups

Annales de l'institut Fourier (1969)

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

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topBerg, 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

top- [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] 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] R.C. BUCK, The measure theoretic approach to density, Amer. J. Math. 68 (1946), p. 560-580. Zbl0061.07503MR8,255f
- [4] J. CIGLER, Folgen normierter Masse auf kompakten Gruppen, Z. Wahrscheinlichkeitstheorie 1 (1962) p. 3-13. Zbl0109.10702MR26 #7012
- [5] E. HEWITT and K.A. ROSS, Abstract Harmonic Analysis, Springer Verlag, Berlin, (1963). Zbl0115.10603
- [6] L.A. RUBEL, Uniform distribution in locally compact Abelian groups, Comm. Math. Helv. 93 (1965), p. 253-258. Zbl0152.03703MR31 #3537
- [7] W. RUDIN, Fourier Analysis in Groups, Interscience Publishers, (1962), New-York. Zbl0107.09603MR27 #2808

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