L2-index and the Selberg trace formula

Journal of Functional Analysis - Tập 53 - Trang 151-201 - 1983
Dan Barbasch1
1Rutgers University, New Brunswick, New Jersey 08903, USA

Tài liệu tham khảo

Arthur, 1974, Some tempered distributions on semisimple groups of real rank one, Ann. of Math., 100, 553, 10.2307/1970958 Atiyah, 1973, On the heat equation and the index theorem, Inventiones Math., 19, 279, 10.1007/BF01425417 Atiyah, 1975, Spectral asymmetry and Riemannian geometry. I, 77, 43 Atiyah, 1977, A geometric construction of the discrete series for sem simple Lie groups, Inventiones Math., 42, 1, 10.1007/BF01389783 Atiyah, 1968, The index of elliptic operators. I, Ann. of Math., 87, 484, 10.2307/1970715 Atiyah, 1968, The index of elliptic operators. III, Ann. of Math., 87, 546, 10.2307/1970717 Barbasch, 1979, Fourier inversion for unipotent invariant integrals, Trans. Amer. Math. Soc, 249, 51, 10.1090/S0002-9947-1979-0526310-9 Barbasch, 1983, The unitary dual for real-rank one semisimple Lie groups, Inventiones Math., 72, 27, 10.1007/BF01389128 Borel, 1980, Stable and L2-cohomology of arithmetic groups, Bull. Amer. Math. Soc. (N. S.), 3, 1025, 10.1090/S0273-0979-1980-14840-5 Bott, 1965, The index theorem for homogeneous differential operators, 167 Connes, 1982, The L2-index theorem for homogeneous spaces of Lie groups, Ann. of Math., 115, 291, 10.2307/1971393 DeGeorge, 1982, On a theorem of Osborne and Warner. Multiplicities in the cuspidal spectrum, J. Funct. Anal., 48, 81, 10.1016/0022-1236(82)90062-3 DeGeorge, 1978, Limit formulas for multiplicities in L2(ΓβG), Ann. of Math., 107, 133, 10.2307/1971140 Gangolli, 1980, Zeta functions of Selberg's type for some noncompact quotients of symmetric spaces of rank one, Nagoya Math. J., 78, 1, 10.1017/S002776300001878X Garland, 1970, Fundamental domains for lattices in R-rank I semisimple Lie groups, Ann. of Math., 92, 279, 10.2307/1970838 Harish-Chandra, 1965, Discrete series for semisimple Lie groups. I, Acta Math., 113, 241, 10.1007/BF02391779 Harish-Chandra, 1966, Discrete series for semisimple Lie groups. II, Acta Math., 116, 1, 10.1007/BF02392813 Hirzebruch, 1958, Automorphe Formen und der Satz von Riemann-Roch, 129 Knapp, 1971, Intertwining operators for semisimple groups, Ann. of Math., 93, 849, 10.2307/1970887 Langlands, 1976, On the functional equations satisfied by Eisenstein series, Vol. 544 Miatello, 1980, The Minakshisundaram-Pleijel coefficients for the vector valued heat kernel on compact locally symmetric spaces of negative curvature, Trans. Amer. Math. Soc., 260, 1 Miatello, 1982, Alternating sum formulas for multiplicities in L2(ΓβG). I, Trans. Amer. Math. Soc., 269, 567 Miatello, 1983, Alternating sum formulas for multiplicities in L2(ΓβG). II, Math. Z., 182, 35, 10.1007/BF01162591 Moscovici, 1982, L2-index of elliptic operators on locally symmetric spaces of finite volume, Vol. 10, 129 Müller, 1980 Nelson, 1959, Analytic vectors, Ann. of Math., 70, 572, 10.2307/1970331 Osborne, 1978, Multiplicities of the integrable discrete series: The case of a non-uniform lattice in an R-rank one semi-simple group, J. Funct. Anal., 30, 287, 10.1016/0022-1236(78)90059-9 Parthasarathy, 1972, Dirac operators and the discrete series, Ann. of Math., 96, 1, 10.2307/1970892 Poulsen, 1972, On C∞-vectors and intertwining bilinear forms for representations of Lie groups, J. Funct. Anal., 9, 87, 10.1016/0022-1236(72)90016-X Ragozin, 1977, On a method for computing multiplicities in L2(ΓβG), Vol. 22 Sally, 1973, The Fourier transform on semisimple Lie groups of real-rank one, Acta Math., 131, 1, 10.1007/BF02392034 Schmid, 1975, Some properties of square-integrable representations of semisimple Lie groups, Ann. of Math., 102, 535, 10.2307/1971043 Selberg, 1956, Harmonic Analysis and discontinuous groups in weakly symmetric spaces with applications to Dirichlet series, J. Indian Math. Soc., 20, 47 Varadarajan, 1973, The theory of characters and the discrete series for semisimple Lie groups, Vol. 24, 45 D. Vogan and G. Zuckerman, Unitary representations with cohomology, preprint. Warner, 1979, Selberg's trace formula for nonuniform lattices: the R-rank one case, Advan. in Math. Suppl. Stud., Vol. 6, 1 F. Williams, Discrete series multiplicities in L2(ΓβG), Amer. J. Math. Zucker, 1982, L2-cohomology of warped products and arithmetic groups, Inventiones Math., 70, 169, 10.1007/BF01390727