Proceedings of the American Mathematical Society

Author(s): Fabio Nicola
Journal: Proc. Amer. Math. Soc. 131 (2003), 2841-2848.
MSC (2000): Primary 46L80; Secondary 58J40, 19K56
Posted: January 8, 2003
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Abstract: We are concerned with the so-called ${\rm SG}$ -pseudo-differential calculus. We describe the spectrum of the unital and commutative $C^\ast$ -algebra given by the norm closure of the space of

-order pseudo-differential operators modulo compact operators; other related algebras are also considered. Finally, their

-theory is computed.

1.: Atiyah M.F., -theory, W.A. Benjamin, New York, 1967. MR 36:7130
2.: Blackadar B., -theory for operator algebras, Springer, New York, 1998. MR 99g:46104
3.: Cordes H.O., A global parametrix for pseudo-differential operators over $\mathbb{R}^n$ , with applications, Reprint, SFB 72, Universität Bonn, 1976.
4.: Cordes H.O., The technique of pseudodifferential operators, Cambridge University Press, 1995. MR 96b:35001
5.: Coriasco S., Fourier integral operators in SG classes. II. Application to SG hyperbolic Cauchy problems, Ann. Univ. Ferrara, 44 (1998), 81-122. MR 2001m:47106
6.: Feygin V.I., Two algebras of pseudodifferential operators in $\mathbb{R}^n$ and some applications, Trudy Moskov. Mat. Obshch., 36 (1977), 155-194.
7.: Grushin V.V., Pseudodifferential operators in $\mathbb{R}^n$ with bounded symbols, Funkc. Anal., 3 (1970), 37-50.
8.: Hörmander L., The analysis of linear partial differential operators III, Springer-Verlag, Berlin, 1985. MR 87d:35002a; corrected reprint MR 95h:35255
9.: Lauter R., Monthubert B., Nistor V., Pseudodifferential analysis on continuous family groupoids, Doc. Math., 5 (2000), 625-655 (electronic). MR 2002f:58046
10.: Lauter R., Moroianu S., Fredholm theory for degenerate pseudodifferential operators on manifolds with fibred boundaries, Commun. P.D.E., 26 (2001), 233-283. MR 2002e:58052
11.: Melo S.T., Nest R., Schrohe E., $C^\ast$ -structure and K-Theory of Boutet de Monvel's algebra, preprint November 2001, Potsdam.
12.: Melrose R.B., Spectral and Scattering theory of the Laplacian on asymptotically Euclidean spaces, in Spectral and Scattering theory, M. Ikawa, ed. Marcel Dekker, 1994, 85-130. MR 95k:58168
13.: Melrose R.B., Geometric scattering theory, Cambridge University Press, 1995. MR 96k:35129
14.: Melrose R.B., Zworski M., Scattering metric and geodesic flow at infinity, Invent. Math., 124 (1996), 389-436. MR 96k:58230
15.: Melrose R.B., Nistor V., -theory of $C^\ast$ -algebras of -pseudodifferential operators, Geom. Funct. Anal., 8 (1998), 88-122. MR 99i:58145
16.: Parenti C., Operatori pseudo-differentiali in $\mathbb{R}^n$ e applicazioni, Annali Mat. Pura Appl., 93 (1972), 359-389. MR 55:10838
17.: Schrohe E., Spaces of weighted symbols and weighted Sobolev spaces on manifolds, vol. 1256 LNM, 360-377, Springer-Verlag, Berlin-Heidelberg, 1987. MR 89g:58200
18.: Schulze B.-W., Boundary Value Problems and Singular Pseudo-differential Operators, J. Wiley & Sons, Chichester, New York, 1998. MR 99m:35281
19.: Shubin M.A., Pseudodifferential operators in $\mathbb{R}^n$ , Dokl. Akad. Nauk SSSR, 196 (1971), 316-319.
20.: Shubin M.A., Pseudodifferential operators and spectral theory, Springer-Verlag, Berlin, . MR 88c:47105
21.: Wegge-Olsen N.E., -theory and $C^\ast$ -algebras, Oxford University Press, New York, 1993. MR 95c:46116

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