Hardy spaces and analytic continuation of Bergman spaces
Bulletin de la Société Mathématique de France, Tome 126 (1998) no. 3, pp. 435-482.
@article{BSMF_1998__126_3_435_0,
     author = {Bertram, Wolfgang and Hilgert, Joachim},
     title = {Hardy spaces and analytic continuation of {Bergman} spaces},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {435--482},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {126},
     number = {3},
     year = {1998},
     doi = {10.24033/bsmf.2332},
     mrnumber = {2000a:32012},
     zbl = {0920.22006},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/bsmf.2332/}
}
TY  - JOUR
AU  - Bertram, Wolfgang
AU  - Hilgert, Joachim
TI  - Hardy spaces and analytic continuation of Bergman spaces
JO  - Bulletin de la Société Mathématique de France
PY  - 1998
SP  - 435
EP  - 482
VL  - 126
IS  - 3
PB  - Société mathématique de France
UR  - http://archive.numdam.org/articles/10.24033/bsmf.2332/
DO  - 10.24033/bsmf.2332
LA  - en
ID  - BSMF_1998__126_3_435_0
ER  - 
%0 Journal Article
%A Bertram, Wolfgang
%A Hilgert, Joachim
%T Hardy spaces and analytic continuation of Bergman spaces
%J Bulletin de la Société Mathématique de France
%D 1998
%P 435-482
%V 126
%N 3
%I Société mathématique de France
%U http://archive.numdam.org/articles/10.24033/bsmf.2332/
%R 10.24033/bsmf.2332
%G en
%F BSMF_1998__126_3_435_0
Bertram, Wolfgang; Hilgert, Joachim. Hardy spaces and analytic continuation of Bergman spaces. Bulletin de la Société Mathématique de France, Tome 126 (1998) no. 3, pp. 435-482. doi : 10.24033/bsmf.2332. http://archive.numdam.org/articles/10.24033/bsmf.2332/

[Ach96] Achab (D.). - Représentations C-dissipatives irréductibles. - Journées ‘Programme de Gelfand-Gindikin', Paris, 1996.

[Be96] Bertram (W.). - On some Causal and conformal Groups, J. Lie Theory, t. 6, 1996, p. 215-244. | MR | Zbl

[Be98] Bertram (W.). - Algebraic Structures of Makarevič Spaces I, Transformation Groups, t. 3, 1998, p. 3-32. | MR | Zbl

[BH97] Bertram (W.), Hilgert (J.). - Reproducing Kernels on Vector Bundles. - Preprint, Clausthal, 1997.

[BO98] Betten (F.), Ólafsson (G.). - Causal compactifications and Hardy spaces of spaces of Hermitian type. - Submitted.

[Cha98] Chadli (M.). - Espace de Hardy d'un espace symétrique de type Cayley, Ann. Inst. Fourier, t. 48, 1998, p. 97-132. | Numdam | MR | Zbl

[Chab90] Chabat (B.). - Introduction à l'analyse complexe, vol. 2. - Éditions MIR, Moscou, 1990. | Zbl

[FK94] Faraut (J.), Korányi (A.). - Analysis on symmetric cones. - Clarendon Press, Oxford, 1994. | MR | Zbl

[FO95] Faraut (J.), Ólafsson (G.). - Causal semi-simple symmetric spaces, the geometry and harmonic analysis, in ‘Semigroups in Algebra, Geometry and Analysis'. - Hofmann, Lawson, Vinberg, eds. ; de Gruyter, Berlin, 1995. | Zbl

[Hw69] Helwig (K.H.). - Involutionen von Jordan-Algebren, Man. Math., t. 1, 1969, p. 211-229. | EuDML | MR | Zbl

[HO96] Hilgert (J.), Ólafsson (G.). - Causal Symmetric Spaces - Geometry and Harmonic Analysis, Perspectives in Math., t. 18, Academic Press, San Diego, 1996. | Zbl

[HOØ91] Hilgert (J.), Ólafsson (G.), Ørsted (B.). - Hardy spaces on affine symmetric spaces, J. reine angew. Math., t. 415, 1991, p. 189-218. | EuDML | MR | Zbl

[JV79] Jakobsen (H.P.), Vergne (M.). - Restriction and Expansion of Holomorphic Representations, J. Functional Analysis, t. 34, 1979, p. 29-53. | MR | Zbl

[Ko68] Kobayashi (S.). - Irreducibility of certain unitary representations, J. Math. Soc. Japan, t. 20, 1968, p. 638-642. | MR | Zbl

[Ko97] Kobayashi (T.). - Multiplicity free theorem in branching problems of unitary highest weight modules, in ‘Proceedings of the annual meeting of Representation Theory at Saga 1997'. - K. Mimachi, ed., p. 9-17.

[KØ96] Koufany (K.), Ørsted (B.). - Function spaces on the Olshanski semi-group and the Gelfand-Gindikin program, Ann. Inst. Fourier, t. 46, 1996, p. 689-722. | EuDML | Numdam | MR | Zbl

[KØ97] Koufany (K.), Ørsted (B.). - Hardy spaces on two-sheeted covering semigroups, J. Lie theory, t. 7, 1997, p. 245-267. | EuDML | MR | Zbl

[Kr97] Krötz (B.). - On Hardy and Bergman spaces on complex Olshanskii semigroups. - Submitted. | Zbl

[La85] Lassalle (M.). - L'espace de Hardy d'un domaine de Reinhard généralisé, J. Funct. Anal., t. 60, 1985, p. 309-340. | MR | Zbl

[Lo77] Loos (O.). - Bounded symmetric domains and Jordan pairs. - Lecture Notes, Irvine, 1977.

[Ma73] Makarevič (B.O.). - Open symmetric orbits of reductive groups in symmetric R-spaces, Math. USSR Sbornik, t. 20, 1973, p. 406-418. | MR | Zbl

[Mo97] Molchanov (V.). - Holomorphic Disrete Series for Hyperboloids of Hermitian Type, J. Funct. Anal., t. 147, 1997, p. 26-50. | MR | Zbl

[Ne98] Neeb (K.H.). - Holomorphy and Convexity in Lie Theory. - de Gruyter, to appear. | MR | Zbl

[OØ91] Ólafsson (G.), Ørsted (B.). - The holomorphic discrete series of an affine symmetric space and representations with reproducing kernel, Trans. Am. Math. Soc., t. 326, 1991, p. 385-405. | MR | Zbl

[OØ98] Ólafsson (G.), Oørsted (B.). - Causal compactifications and Hardy Spaces, Trans. AMS, to appear. | MR | Zbl

[Pe96] Pevsner (M.). - Espace de Bergman d'un semi-groupe complexe, Comptes Rendus Ac. Sci. Paris, Série 1, t. 322, 1996, p. 635-640. | MR | Zbl

[Sa80] Satake (I.). - Algebraic structures of symmetric domains. - Iwanami Shoten, Princeton, 1980. | MR | Zbl

[Ta73] Takeuchi (M.). - Polynomial representations associated with symmetric bounded domains, Osaka J. Math., t. 10, 1973, p. 441-475. | MR | Zbl

Cité par Sources :