Sobolev theory for non commutative tori
Rendiconti del Seminario Matematico della Università di Padova, Tome 86 (1991), pp. 143-156. 
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     author = {Spera, Mauro},
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     pages = {143--156},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {86},
     year = {1991},
     mrnumber = {1154104},
     zbl = {0757.46061},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_1991__86__143_0/}
}
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Spera, Mauro. Sobolev theory for non commutative tori. Rendiconti del Seminario Matematico della Università di Padova, Tome 86 (1991), pp. 143-156. http://archive.numdam.org/item/RSMUP_1991__86__143_0/

[1] R.A. Adams, Sobolev Spaces, Academic Press, New York, London, S. Francisco (1975). | MR | Zbl

[2] M.F. Atiyah - R. BOTT, The Yang Mills equations over Riemann surfaces, Phil. Trans. R. Soc. London A, 308 (1982), pp. 523-625. | MR | Zbl

[3] M.F. Atiyah - I. M. SINGER, The index of elliptic operators: I, Ann. Math., 87 (1968), pp. 484-530. | MR | Zbl

[4] F. Bayen - M. Flato - C. Fronsdal - A. Lichnerowicz - D. Sternhei-Mer, Deformation theory and quantization, I and II, Ann. Phys., 111 (1977), pp. 61-151. | MR | Zbl

[5] J. Bellissard, Ordinary quantum Hall effect and non-commutative cohomology, in Proc. of Localization of Disordered Systems, Bad Schandau 1986, Teubner Publ., Leipzig (1988). | MR

[6] A. Connes, C*-algebres et géometrie différentielle, C. R. Acad. Sci. Paris, Série I, 290 (1980), pp. 599-604. | MR | Zbl

[7] A. Connes, Géométrie non commutative, Interditions, Paris (1990). | MR | Zbl

[8] A. Connes - M. A. Rieffel, Yang Mills for non commutative two tori, in Proceedings of the Conference on Operator Algebras and Mathematical Physics, Univ. of Iowa (1985), Contemporary Mathematics, 62 (1987), pp. 237-266. | MR | Zbl

[9] H. Kosaki, Application of uniform convexity of noncommutative Lp-spaces, Trans. Am. Math. Soc., 283 (1984), pp. 265-282. | MR | Zbl

[10] H.B. Lawson, The theory of gauge fields in four dimensions, Reg. Conf. Ser. Math., 58, Providence, Rhode Island (1985). | MR | Zbl

[11] E. Magenes, Spazi di interpolazione ed equazioni alle derivate parziali, in Atti VII Congresso U.M.I. (Genova, 1963), Ediz. Cremonese, Roma (1964), pp. 134-197. | MR | Zbl

[12] E. Nelson, Notes on non commutative integration, J. Funct. Anal., 15 (1974), pp. 103-116. | MR | Zbl

[13] R. Palais, Foundations of Global non Linear Analysis, Benjamin, New York (1965). | MR | Zbl

[14] G. Pedersen, C*-Algebras and their Automorphism Groups, Academic Press, New York (1979). | MR | Zbl

[15] M.A. Rieffel, C*-algebras associated with irrational rotations, Pac. J. Math., 93 (1981), pp. 415-429. | MR | Zbl

[16] M.A. Rieffel, Projective modules over higher dimensional non commutative tori, Canad. J. Math., 40 (1988), pp. 257-338. | MR | Zbl

[17] M.A. Rieffel, Deformation quantization of Heisenberg manifolds, Commun. Math. Phys., 122 (1989), pp. 531-562. | MR | Zbl

[18] M. Spera, Yang Mills theory in non commutative differential geometry, Rend. Sem. Fac. Sc. Univ. Cagliari, Suppl. Vol. 58 (1988), pp. 409-421. | MR

[19] M. Spera, A symplectic approach to Yang Mills theory for non commutative tori, Canad. J. Math. (to appear). | MR | Zbl

[20] A. Weinstein, Symplectic Groupoids, Geometric Quantization, and Irrational Rotation Algebras, PAM Preprint 1989 (UCBA, Berkeley). | MR | Zbl