Spectrum distribution function and variational principle for automorphic operators on hyperbolic space

D. V. Efremov; M. A. Shubin

Séminaire Équations aux dérivées partielles (Polytechnique) (1988-1989)

  • page 1-19

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Efremov, D. V., and Shubin, M. A.. "Spectrum distribution function and variational principle for automorphic operators on hyperbolic space." Séminaire Équations aux dérivées partielles (Polytechnique) (1988-1989): 1-19. <http://eudml.org/doc/111977>.

@article{Efremov1988-1989,
author = {Efremov, D. V., Shubin, M. A.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {spectrum; distribution function; variational principle; hyperbolic space; periodic operator; Weyl formula; invariant operators; unbounded operators; Sobolev embedding theorem},
language = {eng},
pages = {1-19},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Spectrum distribution function and variational principle for automorphic operators on hyperbolic space},
url = {http://eudml.org/doc/111977},
year = {1988-1989},
}

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)
PY - 1988-1989
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 19
LA - eng
KW - spectrum; distribution function; variational principle; hyperbolic space; periodic operator; Weyl formula; invariant operators; unbounded operators; Sobolev embedding theorem
UR - http://eudml.org/doc/111977
ER -

References

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  1. [A] M.F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras. Astérisque, 32-33 (1976) 43-72. Zbl0323.58015MR420729
  2. [B] A. Borel, Compact Clifford-Klein forms of symmetric spaces. Topology, 2, (1963), 111-122. Zbl0116.38603MR146301
  3. [Br] R. Brooks, The fundamental group and the spectrum of the Laplacian. Comment. Math. Helv., 56 (1981) 581-598. Zbl0495.58029MR656213
  4. [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). Zbl0598.60069MR834169
  5. [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. Zbl0263.47042MR415407
  6. [D-G-M] A. Debiard, B. Gaveau, E. Mazet.Theoremes de Comparison en Geometrie Riemannienne. Publ. RIMS, Kyoto Univ.12 (1976), p.391-425. Zbl0382.31007MR431294
  7. [D] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (algèbres de von Neumann). Paris, Gauthier-Villars, 1969. Zbl0088.32304MR352996
  8. [Don] H. Donnelly, The differential form spectrum of hyperbolic space. Manuscripta math., 33 (1981), 365-385. Zbl0464.58020MR612619
  9. [D-F] H. Donnelly, Ch. Fefferman, L2-cohomology and index theorem for the Bergmann metric. Ann. Math., 118 (1983), 593-618. Zbl0532.58027MR727705
  10. [D-G] J. Duistermaat, V. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics. Invent. Math., 29 (1975), 39-79. Zbl0307.35071MR405514
  11. [E] M.S.P. Eastham, The spectral theory of periodic differential operators. Edinburgh and London, Scottish Acad. Press, 1973. Zbl0287.34016
  12. [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). Zbl0622.35083
  13. [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). Zbl0666.35070
  14. [F-S] B.V. Fedosov, M.A. Shubin, Index of random elliptic operators I. - Matem. Sbornik, v.106 (148) (1978), 108-140. (in Russian). Zbl0409.47030MR501190
  15. [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). Zbl0376.35050MR510082
  16. [Hi] M. Hilsum, Signature operator on Lipschitz manifolds and unbounded Kasparov bi-modules. Lecture Notes in Math., 1132 (1983), 254-288. Zbl0602.46069MR799572
  17. [Hö] L. Hörmander, Analysis of linear partial differential operators, vol. 3. Berlin, Springer, 1985. Zbl0612.35001
  18. [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). Zbl0597.58035MR834168
  19. [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). Zbl0659.35111MR933058
  20. [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). Zbl0647.46049MR856461
  21. [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). 
  22. [Ro] J. Roe, An index theorem on open manifolds I, II. Preprint, Oxford, 1986. Zbl0657.58041MR918459
  23. [S1] R.T. Seeley, Complex powers of an elliptic operator. Proc. Symp. Pure Math., v.10, p.288-307 (1967). Zbl0159.15504MR237943
  24. [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). Zbl0327.35022MR410118
  25. [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). Zbl0493.35041
  26. [Sh3] M.A. Shubin, Pseudodifferential operators and spectral theory. Springer-Verlag, 1987. Zbl0616.47040MR883081
  27. [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). Zbl0431.47027MR535710
  28. [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). Zbl0567.47004MR798454
  29. [T] M. Takesaki, Theory of operator algebras I. Springer Verlag, 1979. Zbl0436.46043MR548728
  30. [V] S.M. Vishik, Some analogs of Riemann (-function. Funkc. Anal. i Ego Pril., 9 (1975), n 3, p.85-86 (in Russian). Zbl0328.58012

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