Geodesic
Quantum Calculus and Quasiconformal Mappings
Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 144-154.

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

The quantum interpretation of quasisymmetric homeomorphisms of the circle, i.e., homeomorphisms that can be extended to quasiconformal homeomorphisms of the unit disk, and their relationship to basic constructions of quantum calculus are discussed.
Keywords: quasisymmetric homeomorphism, Sobolev space of half-differentiable functions
Mots-clés : Connes quantization. 
@article{MZM_2016_100_1_a10,
     author = {A. G. Sergeev},
     title = {Quantum {Calculus} and {Quasiconformal} {Mappings}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {144--154},
     publisher = {mathdoc},
     volume = {100},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a10/}
}
TY  - JOUR
AU  - A. G. Sergeev
TI  - Quantum Calculus and Quasiconformal Mappings
JO  - Matematičeskie zametki
PY  - 2016
SP  - 144
EP  - 154
VL  - 100
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a10/
LA  - ru
ID  - MZM_2016_100_1_a10
ER  - 
%0 Journal Article
%A A. G. Sergeev
%T Quantum Calculus and Quasiconformal Mappings
%J Matematičeskie zametki
%D 2016
%P 144-154
%V 100
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a10/
%G ru
%F MZM_2016_100_1_a10
A. G. Sergeev. Quantum Calculus and Quasiconformal Mappings. Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 144-154. http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a10/

[1] A. Connes, Noncommutative Geometry, Academic Press, San Diego, CA, 1994 | MR | Zbl

[2] A. G. Sergeev, “Lektsii ob universalnom prostranstve Teikhmyullera”, Lekts. kursy NOTs, 21, MIAN, M., 2013, 3–130 | DOI | Zbl

[3] A. G. Sergeev, “Kvantovanie sobolevskogo prostranstva poludifferentsiruemykh funktsii”, Matem. sb., 2016 (to appear)

[4] L. V. Ahlfors, Conformal Invariants, Topics in Geometric Function Theory, McGraw-Hill, New York, 1973 | MR | Zbl

[5] S. C. Power, “Hankel Operators on Hilbert Space”, Research Notes in Math., 64 (1982), Pitman, Boston, MA | MR | Zbl

[6] L. Alfors, Lektsii po kvazikonformnym otobrazheniyam, Mir, M., 1969 | MR | Zbl

[7] O. Lehto, K. I. Virtanen, Quasiconformal Mappings in the Plane, Grundlehren Math. Wiss., 126, Springer-Verlag, Berlin, 1973 | MR | Zbl

[8] S. Nag, D. Sullivan, “Teichmüller theory and the universal period mapping via quantum calculus and the $H^{1/2}$ space on the circle”, Osaka J. Math., 32:1 (1995), 1–34 | MR | Zbl

[9] A. G. Sergeev, “Geometricheskoe kvantovanie prostranstv petel”, Sovr. probl. matem., 13, MIAN, M., 2009, 3–294 | DOI