Mikhail A. Soloviev

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We prove that the Gelfand-Shilov spaces S α are topological algebras under the Moyal star product if and only if α ≥ β. These spaces of test functions can be used in quantum field theory on noncommutative spacetime. The star product depends continuously in their topology on the noncommutativity parameter. We also prove that the series expansion of the Moyal(More)
We examined 38 patients (mean age 55.92 ± 1.56 years) with a 3-5-year history of arterial hypertension. The study showed that hypertension is accompanied by endothelial dysfunction and one of its forming factors is activation of the inflammatory response. Highly sensitive diagnostic tests can verify initiation of inflammation in preclinical manifestations.(More)
We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT symmetry and the standard spin-statistics relation for nonlocal fields, and the regularity properties of the retarded(More)
We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking O(x) =: φ⋆φ : (x) as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x),O(y)] and prove that, in the case of spacespace noncommutativity, it does not vanish at(More)
We prove new theorems about properties of generalized functions defined on Gelfand-Shilov spaces S with 0 ≤ β < 1. For each open cone U ⊂ R we define a space S(U) which is related to S(R) and consists of entire analytic functions rapidly decreasing inside U and having order of growth ≤ 1/(1 − β) outside the cone. Such sheaves of spaces arise naturally in(More)