A new nonformal noncommutative calculus: associativity and finite part regularization
Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 267-297 
@incollection{AST_2008__321__267_0,
     author = {Omori, Hideki and Maeda, Yoshiaki and Miyazaki, Naoya and Yoshioka, Akira},
     title = {A new nonformal noncommutative calculus: associativity and finite part regularization},
     booktitle = {G\'eom\'etrie diff\'erentielle, physique math\'ematique, math\'ematiques et soci\'et\'e (I) : Volume en l'honneur de Jean Pierre Bourguignon},
     editor = {Hijazi Oussama},
     series = {Ast\'erisque},
     pages = {267--297},
     year = {2008},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {321},
     mrnumber = {2521650},
     zbl = {1177.53080},
     language = {en},
     url = {https://www.numdam.org/item/AST_2008__321__267_0/}
}
TY  - CHAP
AU  - Omori, Hideki
AU  - Maeda, Yoshiaki
AU  - Miyazaki, Naoya
AU  - Yoshioka, Akira
TI  - A new nonformal noncommutative calculus: associativity and finite part regularization
BT  - Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon
AU  - Collectif
ED  - Hijazi Oussama
T3  - Astérisque
PY  - 2008
SP  - 267
EP  - 297
IS  - 321
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_2008__321__267_0/
LA  - en
ID  - AST_2008__321__267_0
ER  - 
%0 Book Section
%A Omori, Hideki
%A Maeda, Yoshiaki
%A Miyazaki, Naoya
%A Yoshioka, Akira
%T A new nonformal noncommutative calculus: associativity and finite part regularization
%B Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon
%A Collectif
%E Hijazi Oussama
%S Astérisque
%D 2008
%P 267-297
%N 321
%I Société mathématique de France
%U https://www.numdam.org/item/AST_2008__321__267_0/
%G en
%F AST_2008__321__267_0
Omori, Hideki; Maeda, Yoshiaki; Miyazaki, Naoya; Yoshioka, Akira. A new nonformal noncommutative calculus: associativity and finite part regularization, dans Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 267-297. https://www.numdam.org/item/AST_2008__321__267_0/

[1] G. S. Agarwal & E. Wolf - "Calculus for functions of noncommuting operators and general phase-space methods in quantum mechanics. I. Mapping theorems and ordering of functions of noncommuting operators", Phys. Rev. D 2 (1970), p. 2161-2186. | MR | Zbl | DOI

[2] G. E. Andrews, R. Askey & R. Roy - Special functions, Encyclopedia of Mathematics and its Applications, vol. 71, Cambridge University Press, 1999. | MR | Zbl

[3] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz & D. Sternheimer - "Deformation theory and quantization. I. Deformations of symplectic structures", Ann. Physics 111 (1978), p. 61-110. | MR | Zbl | DOI

[4] I. M. Gel'Fand & G. E. Shilov - Generalized functions. Vol. 2. Spaces of fundamental and generalized functions, Translated from the Russian by Morris D. Friedman, Amiel Feinstein and Christian R Peltzer, Academic Press, 1968. | MR | Zbl

[5] V. Guillemin & S. Sternberg - Geometric asymptotics, Amer. Math. Soc., 1977, Mathematical Surveys, No. 14. | MR | Zbl

[6] Y. Maeda, N. Miyazaki, H. Omori & A. Yoshioka - "Star exponential functions as two-valued elements", in The breadth of symplectic and Poisson geometry, Progr. Math., vol. 232, Birkhäuser, 2005, p. 483-492. | MR | Zbl | DOI

[7] H. Omori - (Physics in Mathematics), Tokyo Univ. Publ., 2004.

[8] H. Omori, "Toward geometric quantum theory", in From geometry to quantum mechanics, Progr. Math., vol. 252, Birkhäuser, 2007, p. 213-251. | MR | Zbl | DOI

[9] H. Omori & T. Kobayashi - "Singular star-exponential functions", SUT J. Math. 37 (2001), p. 137-152. | MR | Zbl

[10] H. Omori & Y. Maeda - (Quantum Theoretic Calculus), Springer, Tokyo, 2004.

[11] H. Omori, Y. Maeda, N. Miyazaki & A. Yoshioka - "Deformation quantization of Fréchet-Poisson algebras: convergence of the Moyal product", in Conférence Moshé Flato 1999, Vol. II (Dijon), Math. Phys. Stud., vol. 22, Kluwer Acad. Publ., 2000, p. 233-245. | MR | Zbl | DOI

[12] H. Omori, Y. Maeda, N. Miyazaki & A. Yoshioka, "Strange phenomena related to ordering problems in quantizations", J. Lie Theory 13 (2003), p. 481-510. | MR | Zbl | EuDML

[13] H. Omori, Y. Maeda, N. Miyazaki & A. Yoshioka, "Expressions of algebra elements and transcendental noncommutative calculus", in Noncommutative geometry and physics 2005, World Sci. Publ., Hackensack, NJ, 2007, p. 3-30. | MR | Zbl | DOI

[14] H. Omori, Y. Maeda, N. Miyazaki & A. Yoshioka, "Geometric objects in an approach to quantum geometry", in From geometry to quantum mechanics, Progr. Math., vol. 252, Birkhäuser, 2007, p. 303-324. | MR | Zbl | DOI

[15] H. Omori, Y. Maeda, N. Miyazaki & A. Yoshioka, "Non-formal deformation quantization of Fréchet-Poisson algebras: the Heisenberg and Lie algebra case", in Geometric and topological methods for quantum field theory, Contemp. Math., vol. 434, Amer. Math. Soc., 2007, p. 99-123. | MR | Zbl | DOI

[16] H. Omori, Y. Maeda, N. Miyazaki & A. Yoshioka, "Noncommutative Minkowski space and transcendental calculus", Progress of Theoretical Physics Suppl. 171 (2007), p. 184-195. | Zbl

[17] H. Omori, Y. Maeda, N. Miyazaki & A. Yoshioka, "Orderings and non-formal deformation quantization", Lett. Math. Phys. 82 (2007), p. 153-175. | MR | Zbl | DOI

[18] M. A. Rieffel - "Noncommutative tori- a case study of noncommutative differentiable manifolds", in Geometric and topological invariants of elliptic operators (Brunswick, ME, 1988), Contemp. Math., vol. 105, Amer. Math. Soc., 1990, p. 191-211. | MR | Zbl | DOI

[19] L. Schwarz - Theory of distributions, Academic Press, 1966.

[20] S. L. Woronowicz - "Differential calculus on compact matrix pseudogroups (quantum groups)", Comm. Math. Phys. 122 (1989), p. 125-170. | MR | Zbl | DOI