Geodesic
A Note on Dirac Operators on the Quantum Punctured Disk
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study quantum analogs of the Dirac type operator $-2\overline z\frac{\partial}{\partial\overline z}$ on the punctured disk, subject to the Atiyah–Patodi–Singer boundary conditions. We construct a parametrix of the quantum operator and show that it is bounded outside of the zero mode.
Keywords: operator theory; functional analysis; non-commutative geometry. 
@article{SIGMA_2010_6_a55,
     author = {Slawomir Klimek and Matt McBride},
     title = {A~Note on {Dirac} {Operators} on the {Quantum} {Punctured} {Disk}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2010},
     volume = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a55/}
}
TY  - JOUR
AU  - Slawomir Klimek
AU  - Matt McBride
TI  - A Note on Dirac Operators on the Quantum Punctured Disk
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2010
VL  - 6
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a55/
LA  - en
ID  - SIGMA_2010_6_a55
ER  - 
%0 Journal Article
%A Slawomir Klimek
%A Matt McBride
%T A Note on Dirac Operators on the Quantum Punctured Disk
%J Symmetry, integrability and geometry: methods and applications
%D 2010
%V 6
%U http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a55/
%G en
%F SIGMA_2010_6_a55
Slawomir Klimek; Matt McBride. A Note on Dirac Operators on the Quantum Punctured Disk. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a55/

[1] Atiyah M. F., Patodi V. K., Singer I. M., “Spectral asymmetry and Riemannian geometry. I”, Math. Proc. Cambridge Philos. Soc., 77 (1975), 43–69 | DOI | MR | Zbl

[2] Booß-Bavnbek B., Wojciechowski K. P., Elliptic boundary problems for Dirac operators, Mathematics: Theory Applications, Birkhäuser Boston, Inc., Boston, MA, 1993 | MR | Zbl

[3] Carey A. L., Klimek S., Wojciechowski K. P., Dirac operators on noncommutative manifolds with boundary, arXiv: 0901.0123

[4] Carey A. L., Phillips J., Rennie A., A noncommutative Atiyah–Patodi–Singer index theorem in KK-theory, arXiv: 0711.3028

[5] Connes A., Non-commutative differential geometry, Academic Press, 1994 | Zbl

[6] Conway J., Subnormal operators, Research Notes in Mathematics, 51, Pitman, Boston, Mass., London, 1981 | MR | Zbl

[7] Halmos P. R., Sunder V. S., Bounded integral operators on $L^2$ spaces, Results in Mathematics and Related Areas, 96, Springer-Verlag, Berlin, New York, 1978 | MR

[8] Klimek S., Lesniewski A., “Quantum Riemann surfaces. III. The exceptional cases”, Lett. Math. Phys., 32 (1994), 45–61 | DOI | MR | Zbl

[9] Klimek S., McBride M., D-bar operators on quantum domains, arXiv: 1001.2216