Abstract
We prove that the Gelfand-Shilov spaces S βα are topological algebras under the Moyal *-product if and only if α ≥ β. These spaces of test functions can be used to construct a noncommutative field theory. The star product depends on the noncommutativity parameter continuously in their topology. We also prove that the series expansion of the Moyal product converges absolutely in S βα if and only if β < 1/2.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 3–17, October, 2007.
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Soloviev, M.A. Star product algebras of test functions. Theor Math Phys 153, 1351–1363 (2007). https://doi.org/10.1007/s11232-007-0119-8
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DOI: https://doi.org/10.1007/s11232-007-0119-8