Abstract:
We show that, for the case of strictly hyperbolic groups, the right-hand side of the Selberg trace formula admits a
representation in the form of a series in the eigenvalues of the Laplacian. The behavior of the Minakshisundaram function as t→0 and t→∞ is studied. Countably many conditions satisfied by the spectrum of the Laplacian are obtained in explicit form.
Keywords:
Selberg formula, strictly hyperbolic group, spectrum of the Laplacian.
Citation:
D. A. Popov, “On the Selberg Trace Formula for Strictly Hyperbolic Groups”, Funktsional. Anal. i Prilozhen., 47:4 (2013), 53–66; Funct. Anal. Appl., 47:4 (2013), 290–301
\Bibitem{Pop13}
\by D.~A.~Popov
\paper On the Selberg Trace Formula for Strictly Hyperbolic Groups
\jour Funktsional. Anal. i Prilozhen.
\yr 2013
\vol 47
\issue 4
\pages 53--66
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\transl
\jour Funct. Anal. Appl.
\yr 2013
\vol 47
\issue 4
\pages 290--301
\crossref{https://doi.org/10.1007/s10688-013-0036-6}
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Linking options:
https://www.mathnet.ru/eng/faa3128
https://doi.org/10.4213/faa3128
https://www.mathnet.ru/eng/faa/v47/i4/p53
This publication is cited in the following 4 articles:
D. A. Popov, “Spectrum of the Laplace operator on closed surfaces”, Russian Math. Surveys, 77:1 (2022), 81–97
D. A. Popov, “O svyazyakh diskretnogo spektra i spektra rezonansov dlya operatora Laplasa na nekompaktnoi giperbolicheskoi rimanovoi poverkhnosti”, Funkts. analiz i ego pril., 53:3 (2019), 61–78
D. A. Popov, “Relationship between the Discrete and Resonance Spectrum for the Laplace Operator on a Noncompact Hyperbolic Riemann Surface”, Funct Anal Its Appl, 53:3 (2019), 205
D. A. Popov, “On the Weyl Formula for the Laplace Operator on Hyperbolic Riemann Surfaces”, Funct. Anal. Appl., 48:2 (2014), 150–153
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