Geodesic
Cohomologies of spaces of Schwartz test functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 3, pp. 323-334

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We calculate cohomologies of the Schwartz algebras $\mathcal{D}$ and $\mathcal{S}$, which are basic spaces (test-function spaces) of the distribution theory. In the process, we find special cohomologies of the quotient algebras $\mathcal{E}/\mathcal{D}$ and $\mathcal{M}/\mathcal{S}$ ($\mathcal{E}$ and $\mathcal{M}$ are also test-function spaces), which are quite unusual from the standpoint of the standard functional analysis and are interesting for theoretical and mathematical physics.
Keywords: Schwartz distribution, cohomology, spherical representation. 
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     author = {V. V. Zharinov},
     title = {Cohomologies of spaces of {Schwartz} test functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {323--334},
     publisher = {mathdoc},
     volume = {170},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_170_3_a0/}
}
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V. V. Zharinov. Cohomologies of spaces of Schwartz test functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 3, pp. 323-334. http://geodesic.mathdoc.fr/item/TMF_2012_170_3_a0/