Geodesic
On formal solutions of the H\"ormander’s initial-boundary value problem in the class of Laurent series
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 3, pp. 278-285.

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We define a derivation of the ring of Laurent series with supports in rational cones and prove existence and uniqueness of a solution to an analog of one initial-boundary value problem of Hörmander for polynomial differential operators with constant coefficients in the class of formal Laurent series.
Keywords: differential operator, the Hörmander’s problem, difference equations
Mots-clés : multiple Laurent series. 
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Evgeny K. Leinartas; Tatiana I. Yakovleva. On formal solutions of the H\"ormander’s initial-boundary value problem in the class of Laurent series. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 3, pp. 278-285. http://geodesic.mathdoc.fr/item/JSFU_2018_11_3_a1/

[1] N.M. Gunther, “On the extension of the Cauchy theorem to any system of partial differential equations”, Mat. sb., 32:2 (1925), 367–447 (in Russian)

[2] A.G. Khovansky, S.P. Chulkov, “The Hilbert and Hilbert-Samuel polynomials and the partial differential equations”, Matem. zametki, 7:1 (2005), 141–151 (in Russian)

[3] A.G. Khovansky, S.P. Chulkov, “The Hilbert polynomial for systems of linear partial differential equations with analytic coefficients”, Izv. RAN. Ser. matem., 70:1 (2006), 163–182 (in Russian)

[4] L. Hörmander, Linear differential operators with partial derivatives, Mir, M., 1965 (in Russian)

[5] T.I. Yakovleva, “Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones”, Sib. Math. J., 58:2 (2017), 363–372

[6] T.I. Nekrasova, “On the Cauchy problem for multidimensional difference equations in rational cone”, Journal of Siberian Federal University, Math. and Phys., 8:2 (2015), 184–191

[7] E.K. Leinartas, T.I. Nekrasova, “Constant coefficient linear difference equations on the rational cones of the integer lattice”, Sib. Math. J., 57:2 (2016), 98–112

[8] E.K. Leinartas, M.S. Rogozina, “Solvability of the Cauchy problem for a polynomial difference operator and monomial bases for the quotients of a polynomial ring”, Sib. Math. J., 56:1 (2015), 111–121

[9] L. Bieberbach, Analytic continuation, Nauka, M., 1967 (in Russian)

[10] L.I. Ronkin, Introduction to the theory of entire functions of several variables, Nauka, M., 1971 (in Russian)