Geodesic
Uniqueness theorem for one class of pseudodifferential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 1, Tome 230 (2023), pp. 50-55

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The uniqueness of solutions for homogeneous equations in the class of analytic functionals $Z'(\mathbb{R}^n)$ with pseudodifferential operators commuting under shifts is discussed. We establish conditions for the symbols of operators that allow one to partition this class of operators into equivalence classes in such a way that within each class, any condition of the regularity of solutions at infinity that guarantees the uniqueness of a solution for an equation with some representative of this class, also guarantees the uniqueness of a solution for equations with all representatives of the same class.
Keywords: pseudo-differential equation, uniqueness of solution
Mots-clés : equivalence 
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     author = {Yu. V. Zasorin},
     title = {Uniqueness theorem for one class of pseudodifferential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {50--55},
     publisher = {mathdoc},
     volume = {230},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_230_a4/}
}
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Yu. V. Zasorin. Uniqueness theorem for one class of pseudodifferential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 1, Tome 230 (2023), pp. 50-55. http://geodesic.mathdoc.fr/item/INTO_2023_230_a4/