Geodesic
Analytic solvability of the H\"ormander problem and the Borel transformation of multiple Laurent series
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 186-195.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, the initial-boundary value problem of Hormander is formulated in the class of functions representable by Laurent series supported in rational cones. Using the Borel transformation of Laurent series we establish a connection between a differential and a difference problems and prove its global analytic solvability.
Keywords: Hörmander problem, polynomial differential operator, difference operator.
Mots-clés : Borel transformation 
@article{JSFU_2022_15_2_a4,
     author = {Evgeny K. Leinartas and Tatiana I. Yakovleva},
     title = {Analytic solvability of the {H\"ormander} problem and the {Borel} transformation of multiple {Laurent} series},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {186--195},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a4/}
}
TY  - JOUR
AU  - Evgeny K. Leinartas
AU  - Tatiana I. Yakovleva
TI  - Analytic solvability of the H\"ormander problem and the Borel transformation of multiple Laurent series
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2022
SP  - 186
EP  - 195
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a4/
LA  - en
ID  - JSFU_2022_15_2_a4
ER  - 
%0 Journal Article
%A Evgeny K. Leinartas
%A Tatiana I. Yakovleva
%T Analytic solvability of the H\"ormander problem and the Borel transformation of multiple Laurent series
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2022
%P 186-195
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a4/
%G en
%F JSFU_2022_15_2_a4
Evgeny K. Leinartas; Tatiana I. Yakovleva. Analytic solvability of the H\"ormander problem and the Borel transformation of multiple Laurent series. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 186-195. http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a4/

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

[2] E.K. Leinartas, T.I. Nekrasova, “Constant coefficient linear difference equations on the rational cones of the integer lattice”, Siberian Mathematical Journal, 57:2 (2016), 98–112 | DOI | MR | Zbl

[3] R. Stanley, Enumerative combinatorics. Trees, generating functions and symmetric functions, Mir, M., 2009 (in Russian) | MR

[4] L. Lipshitz, “D-Finite power series”, Journal of Algebra, 122 (1989), 353–373 | DOI | MR | Zbl

[5] M. Bousquet-Mélou, M. Petkovšek, “Linear recurrences with constant coefficients: the multivariate case”, Discrete Mathematics, 225 (2000), 51–75 | DOI | MR | Zbl

[6] J.W.S. Cassels, Introduction to geometry of numbers, Mir, M., 1965 (in Russian) | MR | Zbl

[7] S. Lang, Algebra, Nauka, M., 1965 (in Russian)

[8] E.K. Leinartas, T.I. Yakovleva, “On formal solutions of the Hormander's initial-boundary value problem in the class of Laurent series”, Journal of Siberian Federal University. Mathematics and Physics, 11:3 (2018), 278–285 | DOI | MR | Zbl

[9] A.A. Znamenskiy, “A refinement of Kovalevskaya's Theorem on analytic solvability of the Cauchy problem”, Journal of Siberian Federal University. Mathematics and Physics, 10:4 (2017), 531–536 | DOI | MR | Zbl

[10] Yu.A. Dubinsky, The Cauchy problem in the complex domain, Izdatelstvo MEI, M., 1996 (in Russian)

[11] L. Bieberbach, Analytic continuation, Nauka, M., 1967 (in Russian) | MR

[12] L.I. Ronkin, Introduction to the theory of entire functions of many variables, Nauka, M., 1971 (in Russian) | MR

[13] V.K. Ivanov, “Growth characteristic of an entire function of two variables and its application to the summation of double power series”, Mat. Sbornik, 47(89):1 (1959), 3–16 (in Russian) | MR

[14] M. Sh.Stavskii, “The relation between the growth of an entire function of several complex variables and the set of singular points of its associated function”, Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2 (1959), 227–232 (in Russian) | MR | Zbl

[15] T.I. Yakovleva, “Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones”, Siberian Mathematical Journal, 58:2 (2017), 363–372 | DOI | MR | Zbl

[16] A.P. Lyapin, S. Chandragiri, “Generating functions for vector partition functions and a basic recurrence relation”, Journal of Difference Equations and Applications, 25:7 (2019), 1052–1061 | DOI | MR | Zbl

[17] E.K. Leinartas, A.P. Lyapin, “On the rationality of multidimensional recurrent power series”, Journal of Siberian Federal University. Mathematics and Physics, 2:4 (2009), 449–455 (in Russian) | Zbl

[18] M.S. Apanovich, E.K. Leinartas, “On correctness of Cauchy problem for a polynomial difference operator with constant coefficients”, The bulletin of Irkutsk state university. Series Mathematics, 26 (2018), 3–15 | DOI | MR | Zbl

[19] E.K. Leinartas, T.I. Yakovleva, “The Cauchy problem for multidimensional difference equations and the preservation of the hierarchy of generating functions of its solutions”, Journal of Siberian Federal University. Mathematics and Physics, 11:6 (2018), 712–722 | DOI | MR | Zbl

[20] M. Forsberg, M. Passare, A. Tsikh, “Laurent Determinants and Arrangements of Hyperplane Amoebas”, Advances in Math., 151 (2000), 45–70 | DOI | MR | Zbl

[21] T.I. Nekrasova, “Sufficient conditions of algebraicity of generating functions of the solutions of multidimensional difference equations”, The bulletin of Irkutsk state university. Series Mathematics, 6:3 (2013), 88–96 (in Russian) | Zbl