Harmonic analysis in weighted L 2 -spaces
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 31 (1998) no. 2, pp. 181-279.
@article{ASENS_1998_4_31_2_181_0,
     author = {Franke, Jens},
     title = {Harmonic analysis in weighted $L_2$-spaces},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {181--279},
     publisher = {Elsevier},
     volume = {Ser. 4, 31},
     number = {2},
     year = {1998},
     doi = {10.1016/s0012-9593(98)80015-3},
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     zbl = {0938.11026},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(98)80015-3/}
}
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Franke, Jens. Harmonic analysis in weighted $L_2$-spaces. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 31 (1998) no. 2, pp. 181-279. doi : 10.1016/s0012-9593(98)80015-3. http://www.numdam.org/articles/10.1016/s0012-9593(98)80015-3/

[Art78] J. G. Arthur, A trace formula for reductive groups I (Duke Mathematical Journal, Vol. 45(4), December 1978, pp. 911-952). | MR | Zbl

[Art80] J. G. Arthur, A trace formula for reductive groups II (Compositio Mathematica, Vol. 40(1), 1980, pp. 87-121). | Numdam | MR | Zbl

[Art82] J. G. Arthur, On the inner product of truncated Eisenstein series (Duke Mathematical Journal, Vol. 49(1), March 1982, pp. 35-50). | MR | Zbl

[Art89] J. G. Arthur, The L²-Lefschetz numbers of Hecke operators (Inventiones Mathematicae, Vol. 97, 1989, pp. 257-290). | MR | Zbl

[Bor66] A. Borel, Reduction theory for arithmetic groups, In Armand Borel and George D. Mostow, editors, Algebraic Groups and Discontinuous Subgroups, Vol. IX of Proceedings of Symposia in Pure Mathematics, pages 20-25, Providence, RI, 1966. American Mathematical Society. | MR | Zbl

[Bor74] A. Borel, Stable real cohomology of arithmetic groups (Annales Scientifiques de l'École Normale Supérieure, Vol. 7:235-272, 1974). | Numdam | MR | Zbl

[Bor83] A. Borel, Regularization theorems in Lie algebra cohomology. Applications (Duke Mathematical Journal, Vol. 50(3), 1983, pp. 605-623). | MR | Zbl

[Bou68] N. Bourbaki, Groupes et algèbres de Lie. Chapitres IV-VI, volume XXXIV of (Éléments de mathématique, Hermann, Paris, 114, Boulevard Saint-Germain, Paris VI, 1968).

[BW80] A. Borel and N. R. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Vol. 94 of (Annals of Mathematics Studies, Princeton University Press and Tokyo University Press, 1980). | MR | Zbl

[Cas] W. Casselman, Paley-Wiener theorems and cohomology, unpublished, Bonn 1984.

[Cas84] W. Casselman, Automorphic forms and a Hodge theory for congruence subgroups of SL2(ℤ) In (Lie group representations II, Vol. 1041 of Lecture Notes in Mathematics, pp. 103-140. Springer, 1984). | MR | Zbl

[Cas89] W. Casselman, Introduction to the Schwartz space of Γ\G (Canadian Journal of Mathematics, Vol. XL(2), pp. 285-320, 1989). | MR | Zbl

[Clo90] L. Clozel, Motifs et formes automorphes : Applications du principe de fonctorialité In L. CLOZEL and J. S. MILNE, editors, (Automorphic Forms, Shimura Varieties, and L-functions I, II, vol. 10-11 of Perspectives in Mathematics, Academic Press, Inc., Vol. I, 1990, pp. 77-159). | MR | Zbl

[Elk90] R. Elkik, Le théorème de Manin-Drinfeld, In L. SZPIRO, editor, (Séminaire sur les Pinceaux de Courbes elliptiques (à la recherche de "Mordell effectif"), Vol. 183 of Astérisque, 1990). | MR | Zbl

[Fra91] J. Franke, A topological model for some summand in the Eisenstein cohomology of congruence subgroups (Preprint 91-090, Bielefeld, Sonderforschungsbereich, Vol. 343, 1991).

[FS91] J. Franke and J. Schwermer, Decomposition of spaces of automorphic forms and rationality properties of automorphic cohomology classes for GLn (Preprint, 1991).

[Gaf51] M. P. Gaffney, The harmonic operator for exterior differential forms (Proc. Nat. Acad. Sci. U.S.A., Vol. 37, 1951, pp. 48-50). | MR | Zbl

[Gro57] A. Grothendieck, Sur quelques points d'algèbre homologique (Tôhoku Mathematical Journal, Second Series, Vol. 9, pp. 119-221, 1957). | MR | Zbl

[Har83] G. Harder, General aspects in the theory of modular symbols, In M.-J. BERTIN, editor, (Séminaire de Théorie des Nombres, Paris 1981-1982, Vol. 38 of Progress in Mathematics, Birkhäuser, 1983, pp. 73-88). | MR | Zbl

[Har86] G. Harder, Der Rang-Eins Beitrag zur Eisensteinkohomologie (Unpublished. Details will appear in a joint book by Harder and Schwermer, 1986).

[Har91] G. Harder, Some results on the Eisenstein cohomology arithmetic subgroups of GLn, J.-P. LABESSE and J. SCHWERMER, editors, (In Cohomology of Arithmetic Groups and Automorphic Forms, Vol. 1447 of Lecture Notes in Mathematics, pp. 85-153. Springer, 1991, Proceedings, Luminy/Marseille 1989). | MR | Zbl

[HC68] Harish-Chandra, Automorphic forms on semi-simple Lie groups, volume 62 of (Lecture Notes in Mathematics, Springer, 1968). | MR | Zbl

[HMSW87] H. Hecht, D. Miličic, W. Schmid, and J. A. Wolf, Localization and standard modules for real semisimple Lie groups I : The duality theorem. (Inventiones Mathematicae, Vol. 90, 1987, pp. 297-332). | MR | Zbl

[JS81] H. Jacquet and J. A. Shalika, Euler products and the classification of automorphic representations II (Amer. J. Math., Vol. 103(4), August 1981, pp. 777-815). | Zbl

[Kna86] A. W. Knapp, Representation theory of semisimple Groups. An overview based on examples (Princeton Mathematical Series, Vol. 36, Princeton University Press, 1986). | MR | Zbl

[Lan76] R. P. Langlands, On the functional equations satisfied by Eisenstein series (Lecture Notes in Mathematics, Vol. 544, Springer, 1976). | MR | Zbl

[Mac71] S. Maclane, Categories for the working mathematician (Graduate Texts in Mathematics, Springer, Vol. 5, 1971). | MR | Zbl

[Mat86] H. Matsumura, Commutative ring theory, volume 8 of (Cambridge studies in advanced mathematics, Cambridge University Press, 1986). | MR | Zbl

[Mül89] W. Müller, The trace class conjecture in the theory of automorphic forms (Ann. of Math. (2), Vol. 130, 1989, pp. 473-529). | MR | Zbl

[MW95] C. Mœglin and J.-L. Waldspurger, Spectral Decomposition and Eisenstein Series (Cambridge tracts in mathematics, Vol. 113, Cambridge University Press, 1995). | MR | Zbl

[OW81] M. S. Osborne and G. Warner, The Theory of Eisenstein Systems (Pure and applied Mathematics, Vol. 99, Academic Press, 1981). | MR | Zbl

[Sch83] J. Schwermer, Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen (Lecture Notes in Mathematics, Vol. 988, Springer, 1983). | MR | Zbl

[Sch94] J. Schwermer, Eisenstein series and the cohomology of arithmetic subgroups : the generic case (Invent. Math., Vol. 116, 1994, pp. 481-511). | MR | Zbl

[Ser65] J.-P. Serre, Algèbre Locale. Multiplicités. Rédigé par P. GABRIEL. Seconde édition (Lecture Notes in Mathematics, Vol. 11, Springer, 1965). | MR | Zbl

[Tri78] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators (North Holland Mathematical Library, Vol. 18, North Holland Publishing Company, Amsterdam, New York, Oxford, 1978). | MR | Zbl

[Vog81] D. A. Vogan, Representations of real reductive Lie groups (Progress in Mathematics, Birkhäuser, Vol. 15, 1981). | MR | Zbl

[VZ84] D. A. Vogan and G. Zuckerman, Unitary representations with continuous cohomology (Compositio Mathematica, Vol. 53, 1984, pp. 51-90). | Numdam | MR | Zbl

[Wal84] N. R. Wallach, On the constant term of square integrable automorphic forms, In (Operator Algebras and Group Representations II, Vol. 18 of Monographs Stud. Math., pp. 227-237. Pitman Publishing, 1984). | MR | Zbl

[Wal88] N. R. Wallach, Real Reductive Groups I (Pure and applied mathematics, Vol. 132, Academic Press, Inc., 1988). | MR | Zbl

[Yos74] Kosaku Yosida, Functional Analysis. Fourth Edition (Grundlehren der mathematischen Wissenschaften, Vol. 123, Springer, 1974). | Zbl

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