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This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses "Leibniz' formulas" with integral remainders or as asymptotic series. A pseudodifferential operator may also be described by invariance under action of a Lie-group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution, and the relation of the hyperbolic theory to the propagation of maximal ideals.
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LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES Managing Editor: Professor J.W.S. Cassels, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England The titles below are available from booksellers, or, in case of difficulty, from Cambridge University Press. 34 36 39 46 50 59 66 69 74 76 77 79 83 86 87 88 89 90 92 93 94 95 96 97 98 99 100 101 103 104 105 106 107 108 109 110 113 114 115 116 117 118 119 121 122 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 Representation theory of Lie groups, M.F. ATIYAH et al Homological group theory, C.T.C. WALL (ed) Affine sets and affine groups, D.G. NORTHCOTT p-adic analysis: a short course on recent work, N. KOBLITZ Commutator calculus and groups of homotopy classes, H.J. BAUES Applicable differential geometry, M. CRAMPIN & F.A.E. PIRANI Several complex variables and complex manifolds II, M.J. FIELD Representation theory, I.M. GELFAND et al Symmetric designs: an algebraic approach, E.S. LANDER Spectral theory of linear differential operators and comparison algebras, H.O. CORDES Isolated singular points on complete intersections, E.J.N. LOOIJENGA Probability, statistics and analysis, J.F.C. KINGMAN & G.E.H. REUTER (eds) Homogeneous structures on Riemannian manifolds, F. TRICERRI & L. VANHECKE Topological topics, I.M. JAMES (ed) Surveys in set theory, A.R.D. MATHIAS (ed) FPF ring theory, C. FAITH & S. PAGE An F-space sampler, N.J. KALTON, N.T. PECK & J.W. ROBERTS Polytopes and symmetry, S.A. ROBERTSON Representation of rings over skew fields, A.H. SCHOFIELD Aspects of topology, I.M. JAMES & E.H. KRONHEIMER (eds) Representations of general linear groups, G.D. JAMES Low-dimensional topology 1982, R.A. FENN (ed) Diophantine equations over function fields, R.C. MASON Varieties of constructive mathematics, D.S. BRIDGES & F. RICHMAN Localization in Noetherian rings, A.V. JATEGAONKAR Methods of differential geometry in algebraic topology, M. KAROUBI & C. LERUSTE Stopping time techniques for analysts and probabilists, L. EGGHE Groups and geometry, ROGER C. LYNDON Surveys in combinatorics 1985, I. ANDERSON (ed) Elliptic structures on 3-manifolds, C.B. THOMAS A local spectral theory for closed operators, I. ERDELYI & WANG SHENGWANG Syzygies, E.G. EVANS & P. GRIFFITH Compactification of Siegel moduli schemes, C-L. CHAI Some topics in graph theory, H.P. YAP Diophantine analysis, J. LOXTON & A. VAN DER POORTEN (eds) An introduction to surreal numbers, H. GONSHOR Lectures on the asymptotic theory of ideals, D. REES Lectures on Bochner-Riesz means, K.M. DAVIS & Y-C. CHANG An introduction to independence for analysts, H.G. DALES & W.H. WOODIN Representations of algebras, P.J. WEBB (ed) Homotopy theory, E. REES & J.D.S. JONES (eds) Skew linear groups, M. SHIRVANI & B. WEHRFRITZ Triangulated categories in the representation theory of finite-dimensional algebras, D. HAPPEL Proceedings of Groups - St Andrews 1985, E. ROBERTSON & C. CAMPBELL (eds) Non-classical continuum mechanics, R.J. KNOPS & A.A. LACEY (eds) Commutator theory for congruence modular varieties, R. FREESE & R. MCKENZIE Van der Corput's method of exponential sums, S.W. GRAHAM & G. KOLESNIK New directions in dynamical systems, T.J. BEDFORD & J.W. SWIFT (eds) Descriptive set theory and t