The energy representation of Sobolev-Lie groups
Albeverio, Sergio ; Høegh-Krohn, Raphael
Compositio Mathematica, Tome S37 (1978), p. 37-51 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{CM_1978__36_1_37_0,
     author = {Albeverio, Sergio and H\o egh-Krohn, Raphael},
     title = {The energy representation of Sobolev-Lie groups},
     journal = {Compositio Mathematica},
     volume = {S37},
     year = {1978},
     pages = {37-51},
     mrnumber = {515036},
     zbl = {0393.22013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1978__36_1_37_0}
}

Albeverio, Sergio; Høegh-Krohn, Raphael. The energy representation of Sobolev-Lie groups. Compositio Mathematica, Tome S37 (1978) pp. 37-51. http://gdmltest.u-ga.fr/item/CM_1978__36_1_37_0/

[1] R.F. Streater: Current commutation relations, continuous tensor products, and infinitely divisible group representations, in Local Quantum theory (R. Jost Ed.), Academic Press, London (1969).

[2] D.H. SHARP, A.S. WIGHTMAN, Edts.: Local Currents and their Applications. North Holland (1974).

[3] C. Newman: Ultralocal quantum field theory in terms of currents. Commun. Math. Phys. 26 (1972) 169-204. | MR 319482

[4] L. Girardello, W. Wyss: Representations of the gauge groups of electrodynamics and general relativity. Helv. Phys. Acta 45, (1972) 97-202 (Fierz Festschrift).

[5] G.F. Dell'Antonio: Lectures on the Thirring model. Acta Phys. Austr. 43 (1975) 43-88. | MR 424115

[6] R.F. Streater: Infinitely divisible representations of Lie algebras. Zeitschr. f. Wahrsch. v. verw. geb. 19 (1971) 67-80. | MR 295715 | Zbl 0199.35202

[7] H. Araki: Factorizable representations of current algebra. Publ. RIMS, Kyoto, Ser. A5 (1970) 361-422. | MR 263326 | Zbl 0238.22014

[8] K.R. Parthasarathy, K. Schmidt: Positive definite kernels, continuous tensor products, and central limit theorems of probability theory. Lecture Notes in Mathematics, Vol. 272, Springer, Berlin (1972). | MR 622034 | Zbl 0237.43005

[9] K. Schmidt: Algebras with quasi local structure and factorizable representations, in Mathematics of Contemporary Physics, R. Streater Edt., Academic Press, London (1972).

[10] J.R. Klauder: Exponential Hilbert space: Fock space revisited. J. Math. Phys. 11 (1970) 609-630. | MR 256673 | Zbl 0187.25801

[11] A. Guichardet: Symmetric Hilbert spaces and related topics. Lecture Notes in Mathematics, Vol. 261, Springer, Berlin (1972). | MR 493402 | Zbl 0265.43008

[12] A.M. Vershik, I.M. Gelfand, M.I. Graev: Representations of the group SL (2, R), where R is a ring of functions. Russ. Math. Surv. 28, No 5 (1973) 83-128. | Zbl 0288.22005

[13] A.M. Vershik, I.M. Gelfand, M.I. Graev: Irreducible representations of the group Gx and cohomology. Funct. Anal. and its Appl. 8, No 2 (1974) 67-69. | MR 348032 | Zbl 0299.22004

[14] A.M. Vershik, I.M. Gelfand, M.I. Graev: Representations of the group of diffeomorphisms connected with infinite configurations. Preprint (1975).

[15] R.C. Ismagilov: On the unitary representations of the group of diffeomorphisms of the space Rn, n ≽ 2. Funct. Anal. and its Appl. 9, No 2 (1975) 71-72. | Zbl 0256.58002

[16] S. Helgason: Differential geometry and symmetric spaces. Academic Press (1962). | MR 145455 | Zbl 0111.18101

[17] R. Gangolli: On the construction of certain diffusions on a differentiable manifold. Z. Wahrscheinlichkeitsth. und verw. geb. 2 (1964) 209-419. | MR 165590 | Zbl 0132.12702

[18] H.P. Mckean: Stochastic integrals. Academic Press (1969). | MR 247684 | Zbl 0191.46603

[19] K. Ito: The Brownian motion and tensor fields on Riemannian manifolds. Proc. Int. Congr. Math. Stockholm (1963) 536-539. | MR 176500 | Zbl 0116.36105