On properties of limits of solutions in the noncommutative sigma model
HTML articles powered by AMS MathViewer
- by
A. V. Domrina;
Translated by: Carl-Fredrik Nyberg Brodda - Trans. Moscow Math. Soc. 2022, 201-215
- DOI: https://doi.org/10.1090/mosc/335
- Published electronically: September 23, 2024
- PDF | Request permission
Abstract:
In this article, sufficient conditions are obtained for the limit of a sequence of solutions converging in the operator norm also to be a solution. It is shown that the extended solutions of such a sequence of solutions converge to an extended solution of the limit. It is also shown that the limit of a sequence of solutions with uniton number 3 can only have uniton number 2 or 3.References
- A. V. Domrin, Noncommutative unitons, Teoret. Mat. Fiz. 154 (2008), no. 2, 220–239 (Russian, with Russian summary); English transl., Theoret. and Math. Phys. 154 (2008), no. 2, 184–200. MR 2424003, DOI 10.1007/s11232-008-0018-7
- A. V. Domrin, Moduli spaces of solutions of a noncommutative sigma model, Teoret. Mat. Fiz. 156 (2008), no. 3, 307–327 (Russian, with Russian summary); English transl., Theoret. and Math. Phys. 156 (2008), no. 3, 1231–1246. MR 2490259, DOI 10.1007/s11232-008-0103-y
- A. V. Domrina, Extended solutions in a noncommutative sigma model, Tr. Mat. Inst. Steklova 279 (2012), no. Analiticheskie i Geometricheskie Voprosy Kompleksnogo Analiza, 72–80 (Russian, with Russian summary); English transl., Proc. Steklov Inst. Math. 279 (2012), no. 1, 64–72. MR 3086758, DOI 10.1134/s0081543812080068
- A. V. Domrina, Integer-valued characteristics of solutions of the noncommutative sigma model, Theoret. and Math. Phys. 178 (2014), no. 3, 265–277. Translation of Teoret. Mat. Fiz. 178 (2014), no. 3, 307–321. MR 3301504, DOI 10.1007/s11232-014-0142-5
- A. V. Domrina, Description of solutions with the uniton number $3$ in the case of one eigenvalue: counterexample to the dimension conjecture, Teoret. Mat. Fiz. 201 (2019), no. 1, 3–16 (Russian, with Russian summary); English transl., Theoret. and Math. Phys. 201 (2019), no. 1, 1413–1425. MR 4017629, DOI 10.4213/tmf9700
- A. V. Domrina and A. V. Domrin, On the dimension of solution spaces of a noncommutative sigma model in the case of uniton number 2, Tr. Mat. Inst. Steklova 298 (2017), no. Kompleksnyĭ Analiz i ego Prilozheniya, 112–126 (Russian, with Russian summary). English version published in Proc. Steklov Inst. Math. 298 (2017), no. 1, 104–117. MR 3725051, DOI 10.1134/S0371968517030086
- Lars Hörmander, The analysis of linear partial differential operators. III, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985. Pseudodifferential operators. MR 781536
Bibliographic Information
- Published electronically: September 23, 2024
- © Copyright 2024 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2022, 201-215
- MSC (2020): Primary 81T10, 81T75
- DOI: https://doi.org/10.1090/mosc/335