Email this article On differential operators an differential equations on torus
- Authors: Burskii V.P1
-
Affiliations:
- Moscow Institute of Physics and Technology (State University)
- Issue: Vol 22, No 4 (2018)
- Pages: 607-619
- Section: Articles
- URL: https://journal-vniispk.ru/1991-8615/article/view/20599
- DOI: https://doi.org/10.14498/vsgtu1659
- ID: 20599
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Abstract
In this paper, we consider periodic boundary value problems for a differential equation whose coefficients are trigonometric polynomials. The spaces of generalized functions are constructed, in which the problems considered have solutions, in particular, the solvability space of a periodic analogue of the Mizohata equation is constructed. A periodic analogue and a generalization of the construction of a nonstandard analysis are constructed, containing not only functions, but also functional spaces. As an illustration of the statement that not all constructions on a torus lead to simplification compared to a plane, a periodic analogue of the concept of a hypoelliptic differential operator is considered, where number-theoretic properties are significant. In particular, it turns out that if a polynomial with integer coefficients is irreducible in the rational field, then the corresponding differential operator is hypoelliptic on the torus.
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##article.viewOnOriginalSite##About the authors
Vladimir P Burskii
Moscow Institute of Physics and Technology (State University)
Email: bvp30@mail.ru
Dr. Phys. & Math. Sci.; Professor; Dept. of Higher Mathematics 9, Inststitutskii per., Dolgoprudny, Moscow region, 141700, Russian Federation
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