Quasi-invariant measures on non-archimedean groups and semigroups of loops and paths, their representations. I

Ludkovsky, Sergey V.

Ludkovsky, Sergey V.

Annales mathématiques Blaise Pascal, Tome 7 (2000) no. 2, pp. 19-53.

MR Zbl

@article{AMBP_2000__7_2_19_0,
     author = {Ludkovsky, Sergey V.},
     title = {Quasi-invariant measures on non-archimedean groups and semigroups of loops and paths, their representations. {I}},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {19--53},
     publisher = {Laboratoires de Math\'ematiques Pures et Appliqu\'ees de l'Universit\'e Blaise Pascal},
     volume = {7},
     number = {2},
     year = {2000},
     mrnumber = {1815165},
     zbl = {0969.43002},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2000__7_2_19_0/}
}

TY  - JOUR
AU  - Ludkovsky, Sergey V.
TI  - Quasi-invariant measures on non-archimedean groups and semigroups of loops and paths, their representations. I
JO  - Annales mathématiques Blaise Pascal
PY  - 2000
SP  - 19
EP  - 53
VL  - 7
IS  - 2
PB  - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
UR  - http://www.numdam.org/item/AMBP_2000__7_2_19_0/
LA  - en
ID  - AMBP_2000__7_2_19_0
ER  -

%0 Journal Article
%A Ludkovsky, Sergey V.
%T Quasi-invariant measures on non-archimedean groups and semigroups of loops and paths, their representations. I
%J Annales mathématiques Blaise Pascal
%D 2000
%P 19-53
%V 7
%N 2
%I Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
%U http://www.numdam.org/item/AMBP_2000__7_2_19_0/
%G en
%F AMBP_2000__7_2_19_0

Ludkovsky, Sergey V. Quasi-invariant measures on non-archimedean groups and semigroups of loops and paths, their representations. I. Annales mathématiques Blaise Pascal, Tome 7 (2000) no. 2, pp. 19-53. http://www.numdam.org/item/AMBP_2000__7_2_19_0/

Bibliographie
Cité par

[1] Y. Amice. "Interpolation p-adique". Bull. Soc. Math. France 92 (1964), 117-180. | Numdam | MR | Zbl

[2] Aref'Eva I.Ya., Dragovich B., Frampton P.H., Volovich I.V. "Wave functions of the universe and p-adic gravity". Int. J. Modern Phys. 6 (1991), 4341-4358. | MR | Zbl

[3] J. Araujo, W.H. Schikhof. "The Weierstrass-Stone approximation theorem for p-adic Cn-functions". Ann. Math. Blaise Pascal. 1 (1994), 61-74. | Numdam | MR | Zbl

[4] N. Bourbaki. "Intégration". Livre VI. Fasc. XIII, XXI, XXIX, XXXV. Ch. 1-9 (Paris: Hermann; 1965, 1967, 1963, 1969).

[5] J.L. Brylinski. "Loop spaces, characteristic classes and geometric quantisation." Progr. in Math. V. 107 (Boston: Birkhaüser, 1993). | MR | Zbl

[6] B. Diarra. "Ultraproduits ultrametriques de corps values". Ann. Sci. Univ. Clermont II, Sér. Math., Fasc. 22 (1984), 1-37. | Numdam | Zbl

[7] H.I. Eliasson. "Geometry of manifolds of maps". J.Difer. Geom. 1 (1967), 169-194. | MR | Zbl

[8] R. Engelking. "General topology". Second Edit., Sigma Ser. in Pure Math. V. 6 (Berlin: Heldermann Verlag, 1989). | MR | Zbl

[9] J.M.G. Fell, R.S. Doran. "Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles". V. 1 and V. 2 (Boston.: Acad. Press, 1988).

[10] E. Hewitt, K.A. Ross. "Abstract harmonic analysis" (Berlin: Springer, 1979). | MR

[11] K. Kunen. "Set theory" (Amsterdam: Nort-Holland Pub.Com.,1980). | MR | Zbl

[12] S.V. Ludkovsky. "Measures on groups of diffeomorphisms of non-Archimedean Banach manifolds". Russ. Math. Surv. 51 (1996), 338-340. | MR | Zbl

[13] S.V. Ludkovsky. "Irreducible unitary representations of non-Archimedean groups of diffeomorphisms". Southeast Asian Math. Bull. 22 (1998), 419-436. | MR | Zbl

[14] S.V. Ludkovsky. "Quasi-invariant and pseudo-differentiable measures on a non-Archimedean Banach space". Int. Cent. Theor. Phys., Trieste, Italy, Preprint N° IC/96/210, 1996.

[15] S.V. Ludkovsky. "Quasi-invariant measures on non-Archimedean loop semigroups". Russ. Math. Surv. 53 (1998), 633-634. | Zbl

[16] S.V. Ludkovsky. "Measures on diffeomorphism groups of non-Archimederan manifolds: group representations and their applications". Theor. and Mathem. Phys. 119 (1999), 381-396. | MR | Zbl

[17] S.V. Ludkovsky. "Gaussian quasi-invariant measures on loop groups and semigroups of real manifolds and their representations". Inst. des Hautes Études Scient., Bures-sur-Yvette, France, Preprint, IHES, Janvier, 1998, 32 pages (shortly in: Dokl. Akad. Nauk (Russian). 370 (2000), 306-308 (N° 3)).

[18] S.V. Ludkovsky. "Embeddings of non-Archimedean Banach manifolds into non-Archimedean Banach spaces". Russ. Math. Surv. 53 (1998), 1097-1098. | Zbl

[19] M.B. Mensky. "The path group. Measurements. Fields. Particles" (Moscow: Nauka, 1983). | MR

[20] L. Narici, E. Beckenstein. "Topological vector spaces" (New York: Marcel Dekker Inc., 1985). | MR | Zbl

[21] A.C.M. Van Rooij. "Non-Archimedean functional analysis" (New York: Marcel Dekker Inc., 1978). | MR | Zbl

[22] W.H. Schikhof. "Ultrametric calculus" (Cambridge: Camb. Univ. Pr., 1984). | MR | Zbl

[23] W.H. Schikhof. "On p-adic compact operators". Report 8911 (Dep. Math. Cath. Univ., Nijmegen, The Netherlands, 1989). | MR

[24] W.H. Schikhof. "A Radon-Nikodym theorem for non-Archimedean integrals and absolutely continuous measures on groups". Indag. Math. 33 (1971), 78-85. | MR | Zbl

[25] R.M. Switzer. "Algebraic topology - homotopy and homology" (Berlin: Springer, 1975). | MR | Zbl

[26] V.S. Vladimirov. "Generalised functions over the field of p-adic numbers". Russ. Math. Surv. 43 (1989), 19-64 (N° 5). | MR | Zbl

[27] V.S. Vladimirov, I.V. Volovich, E.I. Zelenov. "p-Adic analysis and mathematical physics" (Moscow: Fiz.-Mat. Lit, 1994). | Zbl

[28] A. Weil. "Basic number theory" (Berlin: Springer, 1973). | Zbl