Abstract
Kichenassamy found conditions under which the space W p k of differential forms on a closed manifold M embeds compactly in the space F p k of currents on M. We give a version of Kichenassamy's theorem for an arbitrary Banach complex and, in particular, for an elliptic differential complex on a closed manifold.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kichenassamy S., “Compactness theorems for differential forms,” Comm. Pure Appl. Math., 42, No. 1, 47–53 (1989).
Gol′dshtein V. M., Kuz′minov V. I., and Shvedov I. A., “On normal and compact solvability of linear operators,” Sibirsk. Mat. Zh., 30, No. 5, 49–59 (1989).
Kato T., Perturbation Theory for Linear Operators [Russian translation], Mir, Moscow (1972).
Rempel S. and Schuize B.-W., Index Theory of Elliptic Boundary Problems [Russian translation], Mir, Moscow (1986).
Triebel H., Interpolation Theory; Function Spaces; Differential Operators [Russian translation], Mir, Moscow (1980).
Tarkhanov N. N., The Parametrix Method in the Theory of Differential Complexes [in Russian], Nauka, Novosibirsk (1990).
Gol′dshtein V. M., Kuz′minov V. I., and Shvedov I. A., “Integral representation of the integral of a differential form,” in: Functional Analysis and Mathematical Physics [in Russian], Inst. Mat. (Novosibirsk), Novosibirsk, 1985, pp. 53–87.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kuz'minov, V.I., Shvedov, I.A. On the Compactness Theorem for Differential Forms. Siberian Mathematical Journal 44, 107–115 (2003). https://doi.org/10.1023/A:1022020505835
Issue Date:
DOI: https://doi.org/10.1023/A:1022020505835