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Cohomologies of spaces of Schwartz test functions

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Abstract

We calculate cohomologies of the Schwartz algebras D and S, which are basic spaces (test-function spaces) of the distribution theory. In the process, we find special cohomologies of the quotient algebras E/D and M/S (E andMare also test-function spaces), which are quite unusual from the standpoint of the standard functional analysis and are interesting for theoretical and mathematical physics.

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Authors and Affiliations

  1. Steklov Mathematical Institute, RAS, Moscow, Russia

    V. V. Zharinov

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  1. V. V. Zharinov
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Correspondence to V. V. Zharinov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 170, No. 3, pp. 323–334, March, 2012.

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Zharinov, V.V. Cohomologies of spaces of Schwartz test functions. Theor Math Phys 170, 263–273 (2012). https://doi.org/10.1007/s11232-012-0028-3

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  • DOI: https://doi.org/10.1007/s11232-012-0028-3

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