# The convolution equation $P={P}^{*}Q$ of Choquet and Deny and relatively invariant measures on semigroups

Annales de l'institut Fourier (1971)

- Volume: 21, Issue: 4, page 87-97
- ISSN: 0373-0956

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topMukherjea, Arunava. "The convolution equation $P=P^*Q$ of Choquet and Deny and relatively invariant measures on semigroups." Annales de l'institut Fourier 21.4 (1971): 87-97. <http://eudml.org/doc/74063>.

@article{Mukherjea1971,

abstract = {Choquet and Deny considered on an abelian locally compact topological group the representation of a measure $P$ as the convolution product of itself and a finite measure $Q : P = P^*Q$.In this paper, we make an attempt to find, in the case of certain locally compact semigroups, those solutions $P$ of the above equation which are relatively invariant on the support of $Q$. A characterization of relatively invariant measures on certain locally compact semigroups is also presented. Our results on the above convolution equation, when $P$ is finite, have been obtained also by Tortrat in the case of arbitrary topological groups.},

author = {Mukherjea, Arunava},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {4},

pages = {87-97},

publisher = {Association des Annales de l'Institut Fourier},

title = {The convolution equation $P=P^*Q$ of Choquet and Deny and relatively invariant measures on semigroups},

url = {http://eudml.org/doc/74063},

volume = {21},

year = {1971},

}

TY - JOUR

AU - Mukherjea, Arunava

TI - The convolution equation $P=P^*Q$ of Choquet and Deny and relatively invariant measures on semigroups

JO - Annales de l'institut Fourier

PY - 1971

PB - Association des Annales de l'Institut Fourier

VL - 21

IS - 4

SP - 87

EP - 97

AB - Choquet and Deny considered on an abelian locally compact topological group the representation of a measure $P$ as the convolution product of itself and a finite measure $Q : P = P^*Q$.In this paper, we make an attempt to find, in the case of certain locally compact semigroups, those solutions $P$ of the above equation which are relatively invariant on the support of $Q$. A characterization of relatively invariant measures on certain locally compact semigroups is also presented. Our results on the above convolution equation, when $P$ is finite, have been obtained also by Tortrat in the case of arbitrary topological groups.

LA - eng

UR - http://eudml.org/doc/74063

ER -

## References

top- [A] L. N. ARGABRIGHT, A note on invariant integrals on locally compact semigroups, Proc. Amer. Math. Soc., 17 (1966), 377-82. Zbl0138.25602MR32 #5780
- [C-D] G. CHOQUET and J. DENY, Sur l'équation de convolution P = P*Q, C.R. Acad. Sci. Paris, t. 250 (1960), 799-801. Zbl0093.12802MR22 #9808
- [H] E. HEWITT and K. A. ROSS, Abstract Harmonic Analysis, Academic Press, N. Y. (1963). Zbl0115.10603
- [M-T] A. MUKHERJEA and N. A. TSERPES, Idempotent measures on locally compact semigroups Proc. Amer. Math. Soc., Vol. 29, N° 1 (1971), 143-50. Zbl0216.14701MR45 #5268
- [N] K. NUMAKURA, On bicompact semigroups, Math. J. Okayama Univ. 1 (1952), 99-108. Zbl0047.25502MR14,18g
- [T] A. TORTRAT, Lois de probabilité sur un espace topologique complètement régulier et produits infinis à termes indépendants dans un groupe topologique, Ann. Inst. Henri Poincaré, Vol. I, No. 3 (1965), 217-37. Zbl0137.35301MR31 #2755
- [Ti] A. TORTRAT, Lois tendues P sur un demi-groupe topologique complètement simple X, Z. Wahrscheinlichkeitstheorie verw. Geb. 6 (1966), 145-60. Zbl0168.15602MR35 #1063

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