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

Arunava Mukherjea

Annales de l'institut Fourier (1971)

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

Abstract

top
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.

How to cite

top

Mukherjea, 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
  1. [A] L. N. ARGABRIGHT, A note on invariant integrals on locally compact semigroups, Proc. Amer. Math. Soc., 17 (1966), 377-82. Zbl0138.25602MR32 #5780
  2. [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
  3. [H] E. HEWITT and K. A. ROSS, Abstract Harmonic Analysis, Academic Press, N. Y. (1963). Zbl0115.10603
  4. [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
  5. [N] K. NUMAKURA, On bicompact semigroups, Math. J. Okayama Univ. 1 (1952), 99-108. Zbl0047.25502MR14,18g
  6. [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
  7. [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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.