@article{BSMF_1991__119_1_33_0,
author = {Host, Bernard and M\'ela, Jean-Fran\c{c}ois and Parreau, Fran\c{c}ois},
title = {Non singular transformations and spectral analysis of measures},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
pages = {33--90},
year = {1991},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {119},
number = {1},
doi = {10.24033/bsmf.2157},
mrnumber = {93d:43002},
zbl = {0748.43001},
language = {en},
url = {https://www.numdam.org/articles/10.24033/bsmf.2157/}
}
TY - JOUR AU - Host, Bernard AU - Méla, Jean-François AU - Parreau, François TI - Non singular transformations and spectral analysis of measures JO - Bulletin de la Société Mathématique de France PY - 1991 SP - 33 EP - 90 VL - 119 IS - 1 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2157/ DO - 10.24033/bsmf.2157 LA - en ID - BSMF_1991__119_1_33_0 ER -
%0 Journal Article %A Host, Bernard %A Méla, Jean-François %A Parreau, François %T Non singular transformations and spectral analysis of measures %J Bulletin de la Société Mathématique de France %D 1991 %P 33-90 %V 119 %N 1 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2157/ %R 10.24033/bsmf.2157 %G en %F BSMF_1991__119_1_33_0
Host, Bernard; Méla, Jean-François; Parreau, François. Non singular transformations and spectral analysis of measures. Bulletin de la Société Mathématique de France, Tome 119 (1991) no. 1, pp. 33-90. doi: 10.24033/bsmf.2157
[1] . - The eigenvalues of non-singular transformations, Israel J. of Math., t. 45, 1983, p. 297-312. | Zbl | MR
[2] . - The intrinsic normalizing constants of transformations preserving infinite measures, J. Analyse Math., (to appear). | Zbl
[3] and . - L∞ eigenvalues and L2 spectra of non-singular transformations, Proc. London Math. Soc., t. 3 55, 1988, p. 538-570. | Zbl | MR
[4] . - Sur l'ensemble de convergence absolue d'une série trigonométrique, Bull. Soc. Math. France, t. 80 4, 1952, p. 253-317. | Zbl | MR | Numdam
[5] . - A treatise on trigonometric series, vol 2. - Pergamon Press, Oxford, 1964. | Zbl | MR
[6] and . - Products of random variables and Kakutani's criterion for orthogonality of product measures, J. London Math. Soc., t. 2 10, 1975, p. 401-405. | Zbl | MR
[7] and . - Bernoulli measure algebras, Acta Math., t. 132, 1974, p. 77-109. | Zbl | MR
[8] . - Topologie générale, chap. 9. - Hermann, Paris, 1974.
[9] . - Une classification des facteurs de type III, Ann. Sci. École Norm. Sup., t. 6, 1973, p. 133-252. | Zbl | MR | Numdam
[10] . - On the Hierarchy of W. Krieger, Illinois J. of Math., t. 19 3, 1975, p. 428-432. | Zbl | MR
[11] and . - The finite multipliers of infinite ergodic transformations, Lecture Notes in Mathematics, 688, Springer, 1978, p. 127-132. | Zbl | MR
[12] and . - Essays in Commutative Harmonic Analysis. - Springer-Verlag, 1979. | Zbl | MR
[13] , and . - A classification of ergodic non-singular transformation groups, Mem. Fac. Sci. Kyushu Univ., t. A 28, 1974, p. 113-133. | Zbl | MR
[14] , and . - Flows associated with ergodic non-singular transformation groups, Publ. RIMS, Kyoto Univ., t. 11, 1975, p. 31-50. | Zbl | MR
[15] . - Compact groups with ordered duals, VII, J. London Math. Soc., t. 2 20, 1979, p. 509-515. | Zbl | MR
[16] . - Cocycles on the circle, J. Operator Theory, t. 16, 1986, p. 189-199. | Zbl | MR
[17] and . - Cocycles on the circle II. Operator Theory : Advances and Applications, 28 c. - Birkhäuser, 1988. | Zbl | MR
[18] , and . - Analyse harmonique des mesures, Astérisque, 135-136. - Société Mathématique de France, Paris, 1986. | Zbl | MR | Numdam
[19] , and . - Point spectrum and Haussdorff dimension. Number Theory and Combinatorics, p. 209-227 (ed. J. Akiyama et al.). - World Scientific Publishing Co., Tokyo, 1985. | Zbl | MR
[20] and . - Ensembles parfaits et séries trigonométriques. - Hermann, 1963. | Zbl | MR
[21] . - On the equivalence of infinite product measures, Ann. of Math., t. 49, 1948, p. 214-224. | Zbl | MR
[22] and . - On Riesz Product measures : mutual absolute continuity and singularity, Ann. Inst. Fourier, t. 38 2, 1988, p. 63-69. | Zbl | MR | Numdam
[23] . - On ergodic Flows and the Isomorphism of Factors, Math. Ann., t. 223, 1976, p. 19-70. | Zbl | MR
[24] . - Topologie I. - Warszawa-Lwow, 1933.
[25] . - Des produits de Riesz comme mesures spectrales, Ann. Inst. Henri Poincaré, t. 6 4, 1970, p. 335-344. | Zbl | MR | Numdam
[26] and . - Thin sets in Harmonic Analysis, Lecture Notes. - Marcel Dekker, 1971. | Zbl | MR
[27] and . - A class of probability measures arising from some problems in ergodic theory, in Probability measures on groups, Springer Lecture Notes in Mathematics, 706, 1979, p. 124-138. | Zbl | MR
[28] . - Borel structure in groups and their duals, Trans. Am. Math. Soc., t. 85, 1957, p. 134-165. | Zbl | MR
[29] and . - On ergodic quasi-invariant measures on the circle group, J. Funct. Anal., t. 3, 1969, p. 157-163. | Zbl | MR
[30] . - Groupes de valeurs propres des systèmes dynamiques et sous-groupes saturés du cercle, C.R. Acad. Sci. Paris, Série I Math., t. 296, 1983, p. 419-422. | Zbl | MR
[31] . - Quasi-invariant measures and Fourier properties, Commutative Harmonic Analysis, Am. Math. Soc. Contemporary Mathematics, vol. 91, 1989, p. 193-215. | Zbl | MR
[32] and . - Coboundaries and homomorphisms for non-singular group actions and a problem of H. Helson, Proc. London Math. Soc, t. 3 40, 1980, p. 443-475. | Zbl | MR
[33] . - Point spectra of non-singular flows, Publ. Inst. Math. Sci. Kyoto, t. 13, 1977, p. 167-172. | Zbl | MR
[34] . - Ergodicité et pureté des produits de Riesz, Ann. Inst. Fourier, t. 40 2, 1990, p. 391-405. | Zbl | MR | Numdam
[35] . - Measures with real spectra, Inventiones Math., t. 98, 1989, p. 311-330. | Zbl | MR
[36] . - Probability measures on metric spaces. - Academic Press, 1967. | Zbl | MR
[37] . - Étude de quelques propriétés des produits de Riesz, Ann. Inst. Fourier, t. 25 2, 1975, p. 127-169. | Zbl | MR | Numdam
[38] . - Substitution Dynamical Systems, Spectral Analysis. - Springer Lecture Notes, 1294, 1987. | Zbl | MR
[39] . - Fourier Analysis on groups. - Interscience Publishers, 1962. | Zbl | MR
[40] . - Cocycles on ergodic transformation groups. - Macmillan lectures in Math, 1, 1977. | Zbl | MR
[41] . - Spectra of ergodic group actions, Israel J. Math., t. 41, 1982, p. 151-153. | Zbl | MR
[42] . - Geometry of Quantum Theory, vol. II. - Van Nostrand, 1970. | Zbl | MR
[43] . - Groups of continuous functions in Harmonic analysis, Acta Math., t. 125, 1970, p. 109-154. | Zbl | MR
Cité par Sources :







