Shimomura, Hiroaki Unitary representations of the group of diffeomorphisms via restricted product measures with infinite mass. II. (English) Zbl 1242.58005 Publ. Res. Inst. Math. Sci. 48, No. 1, 183-213 (2012). MSC: 58D05 22E65 PDFBibTeX XMLCite \textit{H. Shimomura}, Publ. Res. Inst. Math. Sci. 48, No. 1, 183--213 (2012; Zbl 1242.58005) Full Text: DOI
Shimomura, Hiroaki Positive-definite functions on infinite-dimensional groups. (English) Zbl 1137.58005 Math. Z. 259, No. 2, 355-361 (2008). MSC: 58D20 22E65 58D05 PDFBibTeX XMLCite \textit{H. Shimomura}, Math. Z. 259, No. 2, 355--361 (2008; Zbl 1137.58005) Full Text: DOI
Shimomura, Hiroaki Unitary representations of the group of diffeomorphisms via restricted product measures with infinite mass. (English) Zbl 1117.22011 Heyer, Herbert (ed.) et al., Infinite dimensional harmonic analysis III. Proceedings of the 3rd German-Japanese symposium, University of Tübingen, Tübingen, Germany, September 15–20, 2003. Hackensack, NJ: World Scientific (ISBN 981-256-593-0/hbk). 289-311 (2005). Reviewer: Tomasz Rybicki (Kraków) MSC: 22E65 58D05 PDFBibTeX XMLCite \textit{H. Shimomura}, in: Infinite dimensional harmonic analysis III. Proceedings of the 3rd German-Japanese symposium, University of Tübingen, Tübingen, Germany, September 15--20, 2003. Hackensack, NJ: World Scientific. 289--311 (2005; Zbl 1117.22011)
Shimomura, Hiroaki Irreducible decompositions of unitary representations of infinite-dimensional groups. (English) Zbl 1087.58006 Math. Z. 251, No. 3, 575-587 (2005). Reviewer: Nicolai K. Smolentsev (Kemerovo) MSC: 58D20 22E65 PDFBibTeX XMLCite \textit{H. Shimomura}, Math. Z. 251, No. 3, 575--587 (2005; Zbl 1087.58006) Full Text: DOI
Shimomura, Hiroaki Quasi-invariant measures on the group of diffeomorphisms and smooth vectors of unitary representations. (English) Zbl 0997.58004 J. Funct. Anal. 187, No. 2, 406-441 (2001). Reviewer: Nicolai Konstantinovish Smolentsev (Kemerovo) MSC: 58E05 58A20 22E65 57S05 58D20 PDFBibTeX XMLCite \textit{H. Shimomura}, J. Funct. Anal. 187, No. 2, 406--441 (2001; Zbl 0997.58004) Full Text: DOI
Shimomura, Hiroaki Unitary representations and differential representations of the group of diffeomorphisms and its applications. (English) Zbl 0984.22018 Heyer, Herbert (ed.) et al., Infinite dimensional harmonic analysis. Transactions of the 2nd Japanese-German symposium, University of Kyoto, Japan, September 20-24, 1999. Bamberg: D. u. M. Gräbner, 319-333 (2000). Reviewer: David B.Gauld (Auckland) MSC: 22E65 58H15 PDFBibTeX XMLCite \textit{H. Shimomura}, in: Infinite dimensional harmonic analysis. Transactions of the 2nd Japanese-German symposium, University of Kyoto, Japan, September 20--24, 1999. Bamberg: D. u. M. Gräbner. 319--333 (2000; Zbl 0984.22018)
Shimomura, Hiroaki \(1\)-cocycles on the group of diffeomorphisms. II. (English) Zbl 0952.22009 J. Math. Kyoto Univ. 39, No. 3, 493-527 (1999). Reviewer: D.B.Gauld (Auckland) MSC: 22E65 58D19 57S05 58C35 58B25 58D05 PDFBibTeX XMLCite \textit{H. Shimomura}, J. Math. Kyoto Univ. 39, No. 3, 493--527 (1999; Zbl 0952.22009) Full Text: DOI
Shimomura, Hiroaki Unitary representations and \(1\)-cocycles on the group of diffeomorphisms. (English) Zbl 0943.22018 RIMS Kokyuroku 1082, 48-61 (1999). Reviewer: D.B.Gauld (Auckland) MSC: 22E65 58D05 58B25 PDFBibTeX XMLCite \textit{H. Shimomura}, RIMS Kokyuroku 1082, 48--61 (1999; Zbl 0943.22018)
Shimomura, Hiroaki 1-cocycles on the group of diffeomorphisms. (English) Zbl 0952.58005 J. Math. Kyoto Univ. 38, No. 4, 695-725 (1998). Reviewer: D.B.Gauld (Auckland) MSC: 58B25 22E65 58D05 57S15 PDFBibTeX XMLCite \textit{H. Shimomura}, J. Math. Kyoto Univ. 38, No. 4, 695--725 (1998; Zbl 0952.58005) Full Text: DOI
Tatsuuma, Nobuhiko; Shimomura, Hiroaki; Hirai, Takeshi On group topologies and unitary representations of inductive limits of topological groups and the case of the group of diffeomorphisms. (English) Zbl 0930.22002 J. Math. Kyoto Univ. 38, No. 3, 551-578 (1998). Reviewer: N.Papaghiuc (Iaşi) MSC: 22A05 PDFBibTeX XMLCite \textit{N. Tatsuuma} et al., J. Math. Kyoto Univ. 38, No. 3, 551--578 (1998; Zbl 0930.22002) Full Text: DOI Backlinks: MO
Shimomura, Hiroaki; Hirai, Takeshi On group topologies on the group of diffeomorphisms. (English) Zbl 0949.58001 RIMS Kokyuroku 1017, 104-115 (1997). Reviewer: Nobuaki Obata (MR 99h:58010) MSC: 58B25 22E65 58D05 PDFBibTeX XMLCite \textit{H. Shimomura} and \textit{T. Hirai}, RIMS Kokyuroku 1017, 104--115 (1997; Zbl 0949.58001)
Shimomura, Hiroaki Poisson measures on the configuration space and unitary representations of the group of diffeomorphisms. (English) Zbl 0874.57028 J. Math. Kyoto Univ. 34, No. 3, 599-614 (1994). Reviewer: D.B.Gauld (Auckland) MSC: 57R50 28C20 22E65 58D05 60B05 58D20 PDFBibTeX XMLCite \textit{H. Shimomura}, J. Math. Kyoto Univ. 34, No. 3, 599--614 (1994; Zbl 0874.57028) Full Text: DOI
Shimomura, Hiroaki Ergodic decomposition of measures on a configuration space. (Japanese) Zbl 1095.28514 Yamasaki, Yasuo (ed.), Measure theory on infinite-dimensional spaces, representations of infinite-dimensional groups, and related topics. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, May 17–19, 1994. Kyoto: Kyoto Univ., Research Institute for Mathematical Sciences. RIMS Kôkyûroku 887, 226-242 (1994). MSC: 28D20 37A35 37A40 58D05 60B05 PDFBibTeX XMLCite \textit{H. Shimomura}, in: Measure theory on infinite-dimensional spaces, representations of infinite-dimensional groups, and related topics. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, May 17--19, 1994. Kyoto: Kyoto Univ., Research Institute for Mathematical Sciences. 226--242 (1994; Zbl 1095.28514)