References
[A]M.F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Asterisque, 32–33 (1976), 43–72.
[B]R. Brooks, The fundamental group and the spectrum of the Lapacian, Comment. Math. Helv. 56 (1981), 581–598.
[Ch]P. Chernoff, Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Anal. 12 (1973), 401–414.
[Co]J.M. Cohen, Von Neumann dimension and the homology of covering spaces, Quart. J. Math. 30 (1979), 133–142.
[D]J. Dodziuk, De Rham-Hodge theory forL 2-cohomology of infinite coverings, Topology 16 (1977), 157–165.
[E]A.V. Efremov, Combinatorial and analytic Novikov-Shubin invariants, preprint, 1991.
[ES]D.V. Efremov, M.A. Shubin, Spectrum distribution function and variational principle for automorphic operators on hyperbolic space, Séminaire Equations aux Dérivées Partielles, Ecole Polytechnique, Centre de Mathématiques, Exposé VII, 1988–1989.
[F]D. Fried, Analytic torsion and closed geodesics on hyperbolic manifolds, Invent. Math. 83 (1986), 523–540.
[G]M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES 53 (1981), 53–73.
[K]K. Kodaira, Harmonic fields in Riemannian manifolds, Ann. of Math. 50 (1949), 587–665.
[L]J. Lott, Heat kernels on covering spaces and topological invariants, Preprint IHES/M/90/47, June 1990.
[M]R.J. Miatello, On the Plancherel measure for linear Lie groups of rank one, Manuscripta Math. 29 (1979), 249–276.
[NS1]S.P. Novikov, M.A. Shubin, Morse theory and von Neumann II1-factors, Doklady Akad. Nauk SSSR 289 (1986), 289–292.
[NS2]S.P. Novikov, M.A. Shubin, Morse theory and von Neumann invariants on non-simply connected manifolds, Uspekhi Nauk 41 5 (1986), 222–223, (in Russian).
[RS]M. Reed, B. Simon, Methods of Modern Mathematical Physics, I, Acad. Press, New York e.a., 1972.
[S1]M.A. Shubin, Theorems on the equality of the spectra of a pseudo-differential almost periodic operator inL 2(ℝn) andB 2(ℝn), Sibirsk. Mat. Zh. 17 (1976), 200–215.
[S2]M.A. Shubin, The spectral theory and the index of elliptic operators with almost periodic coefficients, Russian Math. Surveys 34 2 (1979), 109–157.
[T]N. Teleman, The index of signature operators on Lipschitz manifolds, Publications IHES 58 (1983), 39–78.
[Va]N. Varopoulos, Random walks and Brownian motion on manifolds, Symposia Mathematica XXIX (1987), 97–109.
[Vi]S.M. Vishik, Analogs of Selberg's ζ-function, Func. Anal. and Appl. 9, 3 (1975), 256–257.
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Gromov, M., Shubin, M.A. Von Neumann spectra near zero. Geometric and Functional Analysis 1, 375–404 (1991). https://doi.org/10.1007/BF01895640
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DOI: https://doi.org/10.1007/BF01895640