References
S. Zucker, “L 2-cohomology of warped products and arithmetic groups,” Invent. Math.,70, No. 2, 169–218 (1982).
V. M. Gol'dshteįn, V. I. Kuz'minov and I. A. Shvedov, “The Künneth formula forL p -cohomologies of warped products,” Sibirsk. Mat. Zh.,32, No. 5, 29–42 (1991).
V. M. Gol'dshteįn, V. I. Kuz'minov, and I. A. Shvedov, “The reducedL p -cohomologies of warped cylinders,” Sibirsk. Mat. Zh.,31, No. 5, 10–23 (1990).
V. M. Gol'dshteįn, V. I. Kuz'minov, and I. A. Shvedov, “TheL p -cohomologies of warped cylinders,” Sibirsk. Mat. Zh.,31, No. 6, 55–63 (1990).
M. T. Anderson, “L 2-harmonic forms and a conjecture of Dodziuk-Singer,” Bull. Amer. Math. Soc.,13, No. 2, 163–165 (1985).
K. Iosida, Functional Analysis [Russian translation], Mir, Moscow (1967).
V. M. Gol'dshteįn, V. I. Kuz'minov, and I. A. Shvedov, “TheL p -cohomologies of Riemannian manifolds,” in: Studies in Geometry and Mathematical Analysis [in Russian], Nauka, Novosibirsk, 1987, pp. 101–116.
V. M. Gol'dshteįn, V. I. Kuz'minov, and I. A. Shvedov, “Dual spaces of the spaces of differential forms,” Sibirsk. Mat. Zh.,27, No. 1, 45–56 (1986).
K. T. Mynbaev and M. O. Otelbaev, Weighted Functional Spaces and the Spectra of Differential Operators [in Russian], Nauka, Moscow (1988).
V. M. Gol'dshteįn, V. I. Kuz'minov, and I. A. Shvedov, “Normal and compact solvability of linear operators,” Sibirsk. Mat. Zh.,30, No. 5, 49–59 (1989).
V. M. Gol'dshteįn, V. I. Kuz'minov, and I. A. Shvedov, “A property of de Rham regularization operators,” Sibirsk. Mat. zh.,25, No. 2, 104–111 (1984).
H. Donnely and F. Xavier, “On the differential form spectrum on negatively curved Riemannian manifolds,” Amer. J. Math.,106, No. 1, 169–186 (1984).
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Novosibirsk. Translated fromSibirskiį Matematicheskiį Zhurnal, Vol. 33, No. 6, pp. 14–30, November–December, 1992.
Translated by N. S. Dairbekov, V. G. Perepëlkin, and T. N. Rozhkovskaya
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Gol'dshteîn, V.M., Kuz'minov, V.I. & Shvedov, I.A. Nonzero elements in theL p -cohomologies of warped products. Sib Math J 33, 950–965 (1992). https://doi.org/10.1007/BF00971018
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DOI: https://doi.org/10.1007/BF00971018