Non singular transformations and spectral analysis of measures
Bulletin de la Société Mathématique de France, Volume 119 (1991) no. 1, pp. 33-90.
@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},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {119},
     number = {1},
     year = {1991},
     doi = {10.24033/bsmf.2157},
     zbl = {0748.43001},
     mrnumber = {93d:43002},
     language = {en},
     url = {http://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
DA  - 1991///
SP  - 33
EP  - 90
VL  - 119
IS  - 1
PB  - Société mathématique de France
UR  - http://www.numdam.org/articles/10.24033/bsmf.2157/
UR  - https://zbmath.org/?q=an%3A0748.43001
UR  - https://www.ams.org/mathscinet-getitem?mr=93d:43002
UR  - https://doi.org/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://doi.org/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, Volume 119 (1991) no. 1, pp. 33-90. doi : 10.24033/bsmf.2157. http://www.numdam.org/articles/10.24033/bsmf.2157/

[1] Aaronson (J.). - The eigenvalues of non-singular transformations, Israel J. of Math., t. 45, 1983, p. 297-312. | MR | Zbl

[2] Aaronson (J.). - The intrinsic normalizing constants of transformations preserving infinite measures, J. Analyse Math., (to appear). | Zbl

[3] Aaronson (J.) and Nadkarni (M.). - L∞ eigenvalues and L2 spectra of non-singular transformations, Proc. London Math. Soc., t. 3 55, 1988, p. 538-570. | MR | Zbl

[4] Arbault (J.). - Sur l'ensemble de convergence absolue d'une série trigonométrique, Bull. Soc. Math. France, t. 80 4, 1952, p. 253-317. | Numdam | MR | Zbl

[5] Bary (N.). - A treatise on trigonometric series, vol 2. - Pergamon Press, Oxford, 1964. | MR | Zbl

[6] Brown (G.) and Moran (W.). - Products of random variables and Kakutani's criterion for orthogonality of product measures, J. London Math. Soc., t. 2 10, 1975, p. 401-405. | MR | Zbl

[7] Brown (G.) and Moran (W.). - Bernoulli measure algebras, Acta Math., t. 132, 1974, p. 77-109. | MR | Zbl

[8] Bourbaki (N.). - Topologie générale, chap. 9. - Hermann, Paris, 1974.

[9] Connes (A.). - Une classification des facteurs de type III, Ann. Sci. École Norm. Sup., t. 6, 1973, p. 133-252. | Numdam | MR | Zbl

[10] Connes (A.). - On the Hierarchy of W. Krieger, Illinois J. of Math., t. 19 3, 1975, p. 428-432. | MR | Zbl

[11] Furstenberg (H.) and Weiss (B.). - The finite multipliers of infinite ergodic transformations, Lecture Notes in Mathematics, 688, Springer, 1978, p. 127-132. | MR | Zbl

[12] Graham (C.) and Mcgehee (O.C.). - Essays in Commutative Harmonic Analysis. - Springer-Verlag, 1979. | MR | Zbl

[13] Hamachi (T.), Oka (Y.) and Osikawa (M.). - A classification of ergodic non-singular transformation groups, Mem. Fac. Sci. Kyushu Univ., t. A 28, 1974, p. 113-133. | MR | Zbl

[14] Hamachi (T.), Oka (Y.) and Osikawa (M.). - Flows associated with ergodic non-singular transformation groups, Publ. RIMS, Kyoto Univ., t. 11, 1975, p. 31-50. | MR | Zbl

[15] Helson (H.). - Compact groups with ordered duals, VII, J. London Math. Soc., t. 2 20, 1979, p. 509-515. | MR | Zbl

[16] Helson (H.). - Cocycles on the circle, J. Operator Theory, t. 16, 1986, p. 189-199. | MR | Zbl

[17] Helson (H.) and Merrill (K.). - Cocycles on the circle II. Operator Theory : Advances and Applications, 28 c. - Birkhäuser, 1988. | MR | Zbl

[18] Host (B.), Méla (J.F.) and Parreau (F.). - Analyse harmonique des mesures, Astérisque, 135-136. - Société Mathématique de France, Paris, 1986. | Numdam | MR | Zbl

[19] Ito (Y.), Kamae (T.) and Shiokawa. - Point spectrum and Haussdorff dimension. Number Theory and Combinatorics, p. 209-227 (ed. J. Akiyama et al.). - World Scientific Publishing Co., Tokyo, 1985. | MR | Zbl

[20] Kahane (J.P) and Salem (R.). - Ensembles parfaits et séries trigonométriques. - Hermann, 1963. | MR | Zbl

[21] Kakutani (S.). - On the equivalence of infinite product measures, Ann. of Math., t. 49, 1948, p. 214-224. | MR | Zbl

[22] Kilmer (S.J.) and Saeki (S.). - On Riesz Product measures : mutual absolute continuity and singularity, Ann. Inst. Fourier, t. 38 2, 1988, p. 63-69. | Numdam | MR | Zbl

[23] Krieger (W.). - On ergodic Flows and the Isomorphism of Factors, Math. Ann., t. 223, 1976, p. 19-70. | MR | Zbl

[24] Kuratowski (C.). - Topologie I. - Warszawa-Lwow, 1933.

[25] Ledrappier (F.). - Des produits de Riesz comme mesures spectrales, Ann. Inst. Henri Poincaré, t. 6 4, 1970, p. 335-344. | Numdam | MR | Zbl

[26] Lindahl (L.) and Poulsen (F.). - Thin sets in Harmonic Analysis, Lecture Notes. - Marcel Dekker, 1971. | MR | Zbl

[27] Losert (V.) and Schmidt (K.). - 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. | MR | Zbl

[28] Mackey (G.W.). - Borel structure in groups and their duals, Trans. Am. Math. Soc., t. 85, 1957, p. 134-165. | MR | Zbl

[29] Mandrekar (V.) and Nadkarni (M.). - On ergodic quasi-invariant measures on the circle group, J. Funct. Anal., t. 3, 1969, p. 157-163. | MR | Zbl

[30] Méla (J.F.). - 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. | MR | Zbl

[31] Méla (J.F.). - Quasi-invariant measures and Fourier properties, Commutative Harmonic Analysis, Am. Math. Soc. Contemporary Mathematics, vol. 91, 1989, p. 193-215. | MR | Zbl

[32] Moore (C.C.) and Schmidt (K.). - 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. | MR | Zbl

[33] Osikawa (M.). - Point spectra of non-singular flows, Publ. Inst. Math. Sci. Kyoto, t. 13, 1977, p. 167-172. | MR | Zbl

[34] Parreau (F.). - Ergodicité et pureté des produits de Riesz, Ann. Inst. Fourier, t. 40 2, 1990, p. 391-405. | Numdam | MR | Zbl

[35] Parreau (F.). - Measures with real spectra, Inventiones Math., t. 98, 1989, p. 311-330. | MR | Zbl

[36] Parthasarathy (K.R.). - Probability measures on metric spaces. - Academic Press, 1967. | MR | Zbl

[37] Peyrière (J.). - Étude de quelques propriétés des produits de Riesz, Ann. Inst. Fourier, t. 25 2, 1975, p. 127-169. | Numdam | MR | Zbl

[38] Queffélec (M.). - Substitution Dynamical Systems, Spectral Analysis. - Springer Lecture Notes, 1294, 1987. | MR | Zbl

[39] Rudin (W.). - Fourier Analysis on groups. - Interscience Publishers, 1962. | MR | Zbl

[40] Schmidt (K.). - Cocycles on ergodic transformation groups. - Macmillan lectures in Math, 1, 1977. | MR | Zbl

[41] Schmidt (K.). - Spectra of ergodic group actions, Israel J. Math., t. 41, 1982, p. 151-153. | MR | Zbl

[42] Varadarajan (V.S.). - Geometry of Quantum Theory, vol. II. - Van Nostrand, 1970. | MR | Zbl

[43] Varopoulos (N.). - Groups of continuous functions in Harmonic analysis, Acta Math., t. 125, 1970, p. 109-154. | MR | Zbl

Cited by Sources: