Spectrum distribution function and variational principle for automorphic operators on hyperbolic space
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1988-1989), Exposé no. 8, 19 p. 
@article{SEDP_1988-1989____A8_0,
     author = {Efremov, D. V. and Shubin, M. A.},
     title = {Spectrum distribution function and variational principle for automorphic operators on hyperbolic space},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:8},
     pages = {1--19},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     year = {1988-1989},
     mrnumber = {1032284},
     zbl = {0698.35168},
     language = {en},
     url = {http://archive.numdam.org/item/SEDP_1988-1989____A8_0/}
}
TY  - JOUR
AU  - Efremov, D. V.
AU  - Shubin, M. A.
TI  - Spectrum distribution function and variational principle for automorphic operators on hyperbolic space
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:8
PY  - 1988-1989
SP  - 1
EP  - 19
PB  - Ecole Polytechnique, Centre de Mathématiques
UR  - http://archive.numdam.org/item/SEDP_1988-1989____A8_0/
LA  - en
ID  - SEDP_1988-1989____A8_0
ER  - 
%0 Journal Article
%A Efremov, D. V.
%A Shubin, M. A.
%T Spectrum distribution function and variational principle for automorphic operators on hyperbolic space
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:8
%D 1988-1989
%P 1-19
%I Ecole Polytechnique, Centre de Mathématiques
%U http://archive.numdam.org/item/SEDP_1988-1989____A8_0/
%G en
%F SEDP_1988-1989____A8_0
Efremov, D. V.; Shubin, M. A. Spectrum distribution function and variational principle for automorphic operators on hyperbolic space. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1988-1989), Exposé no. 8, 19 p. http://archive.numdam.org/item/SEDP_1988-1989____A8_0/

[A] M.F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras. Astérisque, 32-33 (1976) 43-72. | Numdam | MR | Zbl

[B] A. Borel, Compact Clifford-Klein forms of symmetric spaces. Topology, 2, (1963), 111-122. | MR | Zbl

[Br] R. Brooks, The fundamental group and the spectrum of the Laplacian. Comment. Math. Helv., 56 (1981) 581-598. | MR | Zbl

[B-S] T.E. Bogorodskaja, M.A. Shubin, Variational principle and asymptotic behaviour of the density of states for random pseudodifferential operators. Trudy Sem. Petrovskogo, 11 (1986), 98-117 (in Russian). | MR | Zbl

[C-M-S] L.A. Coburn, L.A. Moyer, I.M. Singer, C*-algebras of almost periodic differential operators. Acta Math., 130 (1973), 279-307. | MR | Zbl

[D-G-M] A. Debiard, B. Gaveau, E. Mazet. Theoremes de Comparison en Geometrie Riemannienne. Publ. RIMS, Kyoto Univ. 12 (1976), p.391-425. | MR | Zbl

[D] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (algèbres de von Neumann). Paris, Gauthier-Villars, 1969. | MR | Zbl

[Don] H. Donnelly, The differential form spectrum of hyperbolic space. Manuscripta math., 33 (1981), 365-385. | MR | Zbl

[D-F] H. Donnelly, Ch. Fefferman, L2-cohomology and index theorem for the Bergmann metric. Ann. Math., 118 (1983), 593-618. | MR | Zbl

[D-G] J. Duistermaat, V. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics. Invent. Math., 29 (1975), 39-79. | MR | Zbl

[E] M.S.P. Eastham, The spectral theory of periodic differential operators. Edinburgh and London, Scottish Acad. Press, 1973. | Zbl

[E-E] A.V. Efremov, D.V. Efremov, The spectrum asymptotics of elliptic operator invariant with respect to discrete group of diffeomorphisms. Vestnik Moskov. Univ. ser.I, Matem., Meh., 1986, n 1, 57-59 (in Russian). | Zbl

[Ef] D.V. Efremov, Spectral function asymptotics of second order elliptic operators on Lobachevsky spaces. Vestnik Moscov. Univ. ser. I, Matem., Meh., 1988, n3, p.72-74 (in Russian). | Zbl

[F-S] B.V. Fedosov, M.A. Shubin, Index of random elliptic operators I. - Matem. Sbornik, v.106 (148) (1978), 108-140. (in Russian). | MR | Zbl

[G] A.I. Gusev, Density of states and other spectral invariants of self-adjoint random elliptic operators.- Matem. Sbornik, 104 (1977), 207-226 (in Russian). | MR | Zbl

[Hi] M. Hilsum, Signature operator on Lipschitz manifolds and unbounded Kasparov bi-modules. Lecture Notes in Math., 1132 (1983), 254-288. | MR | Zbl

[Hö] L. Hörmander, Analysis of linear partial differential operators, vol. 3. Berlin, Springer, 1985. | Zbl

[M-S1] G.A. Meladze, M.A. Shubin, Properly supported uniform pseudodifferential operators on unimodular Lie groups. Trudy Sem. Petrovskogo, 11 (1986), 74-97 (in Russian). | MR | Zbl

[M-S2] G.A. Meladze, M.A. Shubin, Functional calculus of pseudodifferential operators on unimodular Lie groups. Trudy Sem. Petrovskogo,12 (1987), 164-200 (in Russian). | MR | Zbl

[N-S1] S.P. Novikov, M.A. Shubin, Morse inequalities and von Neumann II 1-factors. Doklady Akad. Nauk SSSR, 289 (1986), 289-292 (in Russian). | MR | Zbl

[N-S2] S.P. Novikov, M.A. Shubin, Morse theory and von Neumann invariants of non simply connected manifolds. Uspehi Matem. Nauk, 41(1986), n 5, p.222-223 (in Russian).

[Ro] J. Roe, An index theorem on open manifolds I, II. Preprint, Oxford, 1986. | MR | Zbl

[S1] R.T. Seeley, Complex powers of an elliptic operator. Proc. Symp. Pure Math., v.10, p.288-307 (1967). | MR | Zbl

[Sh1] M.A. Shubin. Weyl theorem for the Schrödinger operator with almost periodic potential. Vestnik Moskov. Univ. ser.I, Mat. Meh. 31 (1976), n 2, 84-88 (in Russian). | MR | Zbl

[Sh2] M.A. Shubin, Density of states of self-adjoint elliptic operators with almost periodic coefficients. Trudy Sem. Petrovskogo, 3 (1978), p.243-275 (in Russian). | Zbl

[Sh3] M.A. Shubin, Pseudodifferential operators and spectral theory. Springer-Verlag, 1987. | MR | Zbl

[Sh4] M.A. Shubin, The spectral theory and index of elliptic operators with almost periodic coefficients. Uspehi Matem. Nauk, 34 (1979), n 2, 95-135. (in Russian). | MR | Zbl

[S] M.M. Skriganov, Geometrical and arithmetical methods in the spectral theory of multydimensional periodic operators. Trudy Matem. Inst. Akad. Nauk SSSR, 171 (1985), Leningrad, Nauka, (in Russian). | MR | Zbl

[T] M. Takesaki, Theory of operator algebras I. Springer Verlag, 1979. | MR | Zbl

[V] S.M. Vishik, Some analogs of Riemann (-function. Funkc. Anal. i Ego Pril., 9 (1975), n 3, p.85-86 (in Russian). | Zbl