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Normal and compact solvability of the exterior differentiation operator under homogeneous boundary conditions

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Literature Cited

  1. J. Cheeger, “On the Hodge theory of Riemannian pseudomanifolds,” Proc. Symp. Pure Math.,36, 91–146 (1980).

    Google Scholar 

  2. G. F. Duff and D. C. Spencer, “Harmonic tensors on Riemannian manifolds (generalized potential theory),” Ann. Math.,50, 587–665 (1949).

    Google Scholar 

  3. A. A. Dezin, “Invariant differential operators and boundary problems,” Tr. Mat. Inst. im. V. A. Steklova Akad. Nauk SSSR,68, 3–88 (1962).

    Google Scholar 

  4. R. S. Saks, “Normally solvable and Noetherian boundary problems for the Maxwell system of equations in the case of steady state processes,” Dokl. Akad. Nauk SSSR,272, No. 2, 308–312 (1983).

    Google Scholar 

  5. N. Teleman, “The index of the signature operator on Lipschitz manifolds,” Publ. Math. I. H. E. S.,58, 39–78 (1983).

    Google Scholar 

  6. M. Hilsum, “Signature operator on Lipschitz manifolds and unbounded Kasparov bimodules,” Lect. Notes Math.,1132, 254–288 (1985).

    Google Scholar 

  7. P. N. Berkhin, “Self-adjoint boundary problem for the system *du+λu=f,” Dokl. Akad. Nauk SSSR,222, No. 1, 15–17 (1975).

    Google Scholar 

  8. T. Kato, Theory of Perturbations of Linear Operators [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  9. V. M. Gol'dshtein, V. I. Kuz'minov, and I. A. Shvedov, “Lp-cohomology of Riemannian manifolds,” in: Research on Geometry and Analysis: Memoirs of the Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR [in Russian], Vol. 7, Novosibirsk (1987), pp. 101–116.

  10. V. M. Gol'dshtein, V. I. Kuz'minov, and I. A. Shvedov “Integral representation of the integral of a differential form,” Functional Analysis and Mathematical Physics [in Russian], Inst. Mat. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1985), pp. 53–87.

    Google Scholar 

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Authors
  1. V. M. Gol'dshtein
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  2. V. I. Kuz'minov
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  3. I. A. Shvedov
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Additional information

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 28, No. 4, pp. 82–96, July–August, 1987.

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Gol'dshtein, V.M., Kuz'minov, V.I. & Shvedov, I.A. Normal and compact solvability of the exterior differentiation operator under homogeneous boundary conditions. Sib Math J 28, 582–593 (1987). https://doi.org/10.1007/BF00973846

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  • DOI: https://doi.org/10.1007/BF00973846

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