Transactions of the Moscow Mathematical Society

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On a class of degenerate hypoelliptic polynomials
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by H. G. Kazaryan and V. N. Margaryan;
Translated by: Kristian B. Kiradjiev
Trans. Moscow Math. Soc. 2022, 151-181
DOI: https://doi.org/10.1090/mosc/337
Published electronically: September 23, 2024
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Abstract:

This work is devoted to finding conditions on “lower-order terms”, the addition of which does not violate the hypoellipticity of a given operator (of the characteristic polynomial of this operator). Necessary and sufficient conditions for the hypoellipticity of “two-layered polynomials” are obtained. In terms of comparing strength, power, and the upper bound of the ratio of comparable polynomials, conditions are obtained under which the added polynomials preserve the hypoellipticity of the original polynomial. Examples are given that illustrate the obtained results.
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Bibliographic Information
  • H. G. Kazaryan
  • Affiliation: Russian-Armenian University; The Institute of Mathematics of National Academy of Sciences of Armenia
  • Email: haikghazaryan@mail.ru
  • V. N. Margaryan
  • Affiliation: Russian-Armenian University
  • Email: vachagan.margaryan@yahoo.com
  • Published electronically: September 23, 2024
  • © Copyright 2024 American Mathematical Society
  • Journal: Trans. Moscow Math. Soc. 2022, 151-181
  • MSC (2020): Primary 12E10, 12D05, 26D05, 35A23
  • DOI: https://doi.org/10.1090/mosc/337