Positive definite kernels on homogeneous spaces and certain stochastic processes related to Lévy's brownian motion of several parameters
Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 3 (1967) no. 2, pp. 121-226. 
@article{AIHPB_1967__3_2_121_0,
     author = {Gangolli, Ramesh},
     title = {Positive definite kernels on homogeneous spaces and certain stochastic processes related to {L\'evy's} brownian motion of several parameters},
     journal = {Annales de l'institut Henri Poincar\'e. Section B. Calcul des probabilit\'es et statistiques},
     pages = {121--226},
     publisher = {Gauthier-Villars},
     volume = {3},
     number = {2},
     year = {1967},
     mrnumber = {215331},
     zbl = {0157.24902},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1967__3_2_121_0/}
}
TY  - JOUR
AU  - Gangolli, Ramesh
TI  - Positive definite kernels on homogeneous spaces and certain stochastic processes related to Lévy's brownian motion of several parameters
JO  - Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques
PY  - 1967
SP  - 121
EP  - 226
VL  - 3
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1967__3_2_121_0/
LA  - en
ID  - AIHPB_1967__3_2_121_0
ER  - 
%0 Journal Article
%A Gangolli, Ramesh
%T Positive definite kernels on homogeneous spaces and certain stochastic processes related to Lévy's brownian motion of several parameters
%J Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques
%D 1967
%P 121-226
%V 3
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1967__3_2_121_0/
%G en
%F AIHPB_1967__3_2_121_0
Gangolli, Ramesh. Positive definite kernels on homogeneous spaces and certain stochastic processes related to Lévy's brownian motion of several parameters. Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 3 (1967) no. 2, pp. 121-226. http://www.numdam.org/item/AIHPB_1967__3_2_121_0/

Ambrose W. [1], The Cartan structure equations in classical Riemannian geometry. Journal of the Indian Mathematical Society, 24, 1960, 23-76. | MR | Zbl

Bargmann V. [1], Unitary representations of the Lorentz group. Annals of Mathematics, 48, 1947, 568-640. | MR | Zbl

Belayev Yu K.. [1], Continuity and Hölder's conditions for sample functions of stationary Gaussian processes. Proceedings of the fourth Berkeley symposium in Mathematical Statistics and Probability Theory, vol. 2. University of California Press. Berkeley, 1961, 23-34. | Zbl

Bochner S. [1], Harmonic analysis and the theory of probability. University of California Press. Berkeley, 1955. | MR | Zbl

Cartan É.. [1], Sur la détermination d'un système orthogonal complet dans un espace de Riemann symétrique clos. Circolo matematico di Palermo, Rendiconti, 53, 1929, 217-252. | JFM

Chentsov N.N. [1], Lévy's Brownian motion of several parameters and generalized white noise. Theory of probability and its applications, 2, 1957, 265-266.

Delsarte J. [1], Une extension nouvelle de la théorie des fonctions presque périodiques de Bohr. Acta Mathematica, 69, 1938, 259-317. | JFM | Zbl

Edwards R.E. and Hewitt E. [1], Pointwise limits for sequences of convolution operators. Acta Mathematica (Stockholm), 113, 1965, 181-218. | MR | Zbl

Erdelyi A., Magnus W., Oberhettinger C. and Tricomi F. [1], Higher Transcendental Functions, vol. 2 (Bateman Manuscript project) McGraw-Hill, New York, 1953.

Furstenberg H. [1], Noncommuting random products. Transactions of the American Mathematical Society, 108, 1963, 377-428. | MR | Zbl

Gangolli R. [1], Isotropic infinitely divisible measures on symmetric spaces. Acta Mathematica (Stockholm), 111, 1964, 213-246. | MR | Zbl

Gangolli R. [2], The sample functions of certain differential processes on symmetric spaces. Pacific Journal of Mathematics, 15, 1965, 477-496. | MR | Zbl

Gangolli R. [3], Abstract harmonic analysis and Lévy's Brownian motion of several parameters: Proceedings of the fifth Berkeley symposium in Mathematical Statistics and Probability Theory. University of California Press, Berkeley (To appear). | Zbl

Godement R. [1], Les fonctions du type positif et la théorie des groupes. Transactions of the American Mathematical Society, 63, 1948, 1-84. | MR | Zbl

Godement R. [2], Introduction aux travaux de A. Selberg. Séminaire Bourbaki, Exposé 144, Paris, 1957. | Numdam | Zbl

Helgason S. [1], Differential geometry and symmetric spaces. Academic Press, New York, 1962. | MR | Zbl

Helgason S. [2], The Radon transform for Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds. Acta Mathematica (Stockholm), 113, 1965, 153-180. | MR | Zbl

Herz C. [1], The spectral theory of bounded functions. Transactions of the American Mathematical Society, 94, 1960, 181-232. | MR | Zbl

Hida T. [1], Canonical representations of Gaussian processes and their applications. Memoirs of the college of Science. University of Kyotô. Series A. 23, 1960, 109-155. | MR | Zbl

Hirschman I.I. [1], Sur les polynômes ultrasphériques. Comptes Rendus de l'Académie des Sciences, Paris, 242, 1956, 2212-2215. | MR | Zbl

Itô K. [1], Isotropic random current. Proceedings of the third Berkeley symposium in Mathematical Statistics and Probability Theory, vol. 2, University of Califormia Press, 1956, 125-132. | MR | Zbl

Kennedy M. [1], A stochastic process associated with the ultraspherical polynomials. Proceedings of the Royal Irish Academy, section A, 64, 1961, 89-100. | MR | Zbl

Krein M.G. [1], Hermitian positive kernels on homogeneous spaces, I, II. Ame- rican Mathematical Society translations, series 2, vol. 34, 1963. | MR | Zbl

Levitan B.M. [1], The application of generalized displacement operators to linear differential equations of the second order. American Mathematical Society Translation, no. 59, Providence, R. I., 1951. | MR

Lévy P. [1], Processus Stochastiques et Mouvement Brownien. Gauthier-Villars, Paris, 1947. | MR | Zbl

Lévy P. [2], A special problem of Brownian motion and a general theory of Gaussian random functions. Proceedings of the third Berkeley symposium in Mathematical Statistics and Probability Theory, vol. 2. University of California Press, Berkeley, 1956, 133-175. | MR | Zbl

Lévy P. [3], Brownian motion depending on n parameters. The particular case n = 5. Proceedings of the symposia in applied mathematics. American Mathematical Society. Providence, R. I., 1957. | MR | Zbl

Lévy P. [4], Le mouvement brownien fonction d'un point de la sphère de Riemann: Circolo matematico di Palermo, Rendiconti, ser. 2,8, 1959, 297-310. | Zbl

Loéve M. [1], Probability Theory. D. Van Nostrand Co. Princeton, 1963 (Third edition). | MR | Zbl

Loomis L. [1], Abstract harmonic analysis. D. Van Nostrand Co. Princeton, N. J., 1953. | MR | Zbl

Mckean H.P. Jr. [1], Brownian motion with a several dimensional time. Teoria Veroyatnostei, 8, 1963, 357-378. | MR | Zbl

Naimark M.A. [1], Normed rings (English translation). P. Noordhoff and Ltd. Amsterdam, 1960. | MR | Zbl

Parthasarathy K.R., Ranga Rao R. and Varadhan S.R.S. [1], Probability distributions on locally compact abelian groups. Illinois Journal of Mathematics, 7, 1963, 377-378. | MR | Zbl

Prohorov Yu V.. [1], Characteristic functionals. Proceedings of the fourth Berkeley symposium in Mathematical statistics and Probability theory. University of California Press, Berkeley, 1961, 403-419. | Zbl

Prohorov Yu. V. [2], Convergence of random processes and limit theorems in probability theory. Teoria Veroyatnostei, i ee Primenenia, 1, 1956, 177-238. | MR | Zbl

Robin L. [1], Fonctions sphériques de Legendre et fonctions sphéroïdales. Tome II. Gauthier-Villars, Paris, 1958. | MR | Zbl

Rogalski Marc [1], Le théorème de Lévy-Khincin. Séminaire Choquet, Paris, 1963-1964. Exposé 2. | Numdam | MR | Zbl

Schoenberg I.J. [1], Metric spaces and positive definite functions. Trans. Amer. Math. Soc., 44, 1938, 522-536. | JFM | MR | Zbl

Schoenberg I.J. [2], Metric spaces and completely monotone functions. Annals of Mathematics, 39, 1938, 811-841. | JFM | MR | Zbl

Tits J. [1], Sur certaines classes d'espaces homogènes de groupes de Lie. Acad. Roy. Belg. cl. Sci. Mem. Coll., 29, 1955, no. 3. | MR | Zbl

Varadhan S.R.S.. [1], Limit theorems for sums of independent random variables with values in a Hilbert space. Sankhya, 24, 1962, 213-238. | MR | Zbl

Vilenkin N.Ya. [1], Matrix-elements of irreducible unitary representations of the group of Lobachevsky space motions and the generalized Fock-Mehler transform. Dokladi Akademii Nauk, SSSR, 118, 1958, 219-222. | MR | Zbl

Wang H.C. [1], Two-point homogeneous spaces. Annals of Mathematics, 55, 1952, 177-191. | MR | Zbl

Weil A. [1], L'intégration dans les groupes topologiques et ses applications. Hermann, Paris, 1940. | JFM | Zbl

Wolf J.A. [1], Self-adjoint function spaces on Riemannian symmetric manifolds. Transactions of the American Mathematical Society, 113, 1964, 299-315. | MR | Zbl

Yaglom A.M. [1], Some classes of random fields in n-dimensional Euclidean space related to stationary random processes. Theory of probability and its applications (English Translation), 2, 1957, 273-320. | Zbl

Yaglom A.M. [2], Second-order homogeneous random fields. Froceedings of the fourth Berkeley symposium in Mathematical Statistics and Probability Theory, vol. 2. University of California Press, 1961, 593-622. | MR | Zbl