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Holomorphic representation theory. I

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References

  1. Aronszajn, N., Theory of reproducing kernels, Trans. Am. Math. Soc.68 (1950), 337–404

    Google Scholar 

  2. Berg, C., Christensen, J.P.R., P. Ressel, “Harmonic analysis on semigroups”. Grad. Texts Math., Springer 1984

  3. Bourbaki, N., Groupes et algèbres de Lie, Chapitres 7 et 8. Masson, Paris 1990

    Google Scholar 

  4. Brunet, M., P. Kramer, Semigroups of length increasing transformations. Rep. Math. Phys.15 (1979), 287–304

    Google Scholar 

  5. Brunet, M., P. Kramer, Complex extensions of the representation of the symplectic group associated with the canonical commutation relations. Rep. Math. Phys.17 (1980), 205–215

    Google Scholar 

  6. Brunet, M., The metaplectic semigroup and related topics. Rep. Math. Phys.22 (1985), 149–170

    Google Scholar 

  7. Dixmier, J., “LesC *-algèbres et leurs représentations”. Gauthier-Villars, Paris 1964

    Google Scholar 

  8. Dixmier, J., Sur la representation régulière d'un groupe localement compact connexe. Ann. Sci. Éc. Norm. Supér., 4e Sér.2 (1969), 423–436

    Google Scholar 

  9. Fell, J.M.G., R.S. Doran, “Representations of *-Algebras, Locally Compact Groups, and Banach-*-Algebraic Bundles”, vol. I, II. Pure Appl. Math.125, 126, Academic Press 1988

  10. Folland, G.B., “Harmonic Analysis in Phase Space”. Princeton University Press, Princeton, NJ 1989

    Google Scholar 

  11. Goodman, R., Analytic and entire vectors for representations of Lie groups. Transa. Am. Math. Soc.143 (1969), 55–76

    Google Scholar 

  12. Hilgert, J., A note on Howe's oscillator semigroup Ann. Institut Fourier39 (1989), 663–688

    Google Scholar 

  13. Hilgert, J., K.H. Hofmann, Compactly embedded Cartan Algebras and Invariant Cones in Lie Algebras. Adv. Math.75 (1989) 168–201

    Google Scholar 

  14. Hilgert, J., K.H. Hofmann, J.D. Lawson, “Lie Groups, Convex Cones, and Semigroups”. Oxford University Press 1989

  15. Hilgert, J., K.-H. Neeb, “Lie-Gruppen und Lie-Algebren”. Vieweg, Braunschweig 1991

    Google Scholar 

  16. Hilgert, J., K.-H. Neeb, “Lie semigroups and their Applications”. Springer Lect. Notes Math.1552 (1993)

  17. Hilgert, J., G. Olafsson, Analytic continuations of representations, the solvable case. Jap. Math.18 (1992), 213–290

    Google Scholar 

  18. Hilgert, J., Olafsson, G., B. Ørsted, Hardy Spaces on Affine Symmetric Spaces. J. Reine Angew. Math.415 (1991), 189–218

    Google Scholar 

  19. Hochschild, G.P., “The Structure of Lie Groups”. Holden Day, San Francisco 1965

    Google Scholar 

  20. Howe, R., The Oscillator semigroup. In: “The Mathematical Heritage of Hermann Weyl”. Proc. Symp. Pure Math.48, R.O. Wells Ed., Am. Math. Soc., Providence 1988

    Google Scholar 

  21. Lawson, J.D., Polar and Ol'shanskiî decompositions. Seminar Sophus Lie1:2 (1991), 163–173

    Google Scholar 

  22. Lawson, J.D., Polar and Ol'shanskiî decompositions. J. Reine Angew. Math.448 (1994), 191–219

    Google Scholar 

  23. Loos, O., “Symmetric Spaces I: General Theory”. Benjamin, New York, Amsterdam 1969

    Google Scholar 

  24. Neeb, K.-H., The Duality between subsemigroups of Lie groups and monotone function. Trans. Am. Math. Soc.329 (1992), 653–677

    Google Scholar 

  25. Neeb, K.-H., On the fundamental group of a Lie semigroup. Glasg. Math. J.34 (1992), 379–394

    Google Scholar 

  26. Neeb, K.-H., Invariant subsemigroups of Lie groups. Mem. Am. Math. Soc.499, 1993

  27. Neeb, K.-H., Contraction semigroups and representations, Forum Math.6 (1994), 233–270

    Google Scholar 

  28. Neeb, K.-H., Representations of involutive semigroups. Semigroup Forum48 (1994), 197–218

    Google Scholar 

  29. Neeb, K.-H., On closedness and simple connectedness of adjoint and coadjoint orbits. Manuscr. Math.82, (1994), 51–65

    Google Scholar 

  30. Neeb, K.-H. Holomorphic representation theory II. Acta Math. (to appear)

  31. Neeb, K.-H. The classification of Lie algebras with invariant cones. (submitted)

  32. Neeb, K.-H., Coherent states, holomorphic extensions, and unitary highest weight representations. Pac. J. Math., (to appear)

  33. Ol'shanskiî, G.I., Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series. Funct. Anal. Appl.15 (1982), 275–285

    Google Scholar 

  34. Penney, R., The entire vectors and holomorphic extensions of representations. Transa. Am. Math. Soc.198 (1974), 107–121

    Google Scholar 

  35. Rothstein, W., K. Kopfermann, “Funktionentheorie mehrerer komplexer Veränderlicher”, B.I. Wissenschaftsverlag, Mannheim, Wien, Zürich 1982

    Google Scholar 

  36. Stanton, R.J., Analytic Extension of the holomorphic discrete series. Am. J. Math.108 (1986), 1411–1424

    Google Scholar 

  37. Sugiura M., “Unitary representations and Harmonic Analysis — An introduction-”. Wiley, New York, London, Sydney, Toronto 1975

    Google Scholar 

  38. Wallach, N.R., “Real reductive groups II”. Academic Press, Boston, New York, Tokyo 1992

    Google Scholar 

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  1. Fachbereich Mathematik, Arbeitsgruppe 5, Technische Hochschule Darmstadt, Schlossgartenstrasse. 7, D-64289, Darmstadt, Germany

    Karl-Hermann Neeb

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Neeb, KH. Holomorphic representation theory. I. Math. Ann. 301, 155–181 (1995). https://doi.org/10.1007/BF01446624

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