190 INDEX odd-class symbols, 18 order of a symbol, 17 order of an operator, 116 Paneitz operators, 175 period, 38 pointwise conformally covariant of weight, 177 Polyakov action, 181 polyhomogeneous operator, 111 polyhomogeneous symbol, 17, 85 primitive lattice vectors, 83 principal angle, 131 properly supported symbol, 110 properly supported operator, 110 pseudodifferential operator, 108, 109, 115 pseudolocality, 109 Q-curvature, 175 Q-weighted determinant, 167 quotient Fr´ echet topology on formal classical symbols, 19 Rd-translation invariant set/linear form, 30 R-regularised discrete sum, 96 R-regularised integral, 71 R-regularised trace, 135 regular integral polytopes, 83 regular linear form, 122 regularised evaluator, 54 regularised Euler-Maclaurin formula, 96 rescaling invariant linear form, 41 rescaling invariant set, 41 residue determinant, 155 Riesz extension of Gamma function, 7 Riesz regularisation, 5, 70 Rota-Baxter operator, 54 Rota-Baxter relation, 54 Schwartz functions on Rd, 16 Schwartz functions on R+, 1 simple integral polytopes, 83 singular linear form on operators, 122 singular linear form on symbols, 20 singular support of a distribution, 109 smoothing operator, 108, 115 smoothing symbol, 16 star-product, 112 Stokes’ property on symbols, 23 Stokes’ theorem, 23 symbol valued differential forms, 22 symbolically defined set of operators, 121 symbols with constant coeﬃcients, 15 Todd function, 80 trace of a smoothing operator, 115 translation invariant linear form on symbols, 30 translation invariant set of symbols, 30 twisted Dirac operator, 162 twisted Z2-graded spinor bundle, 162 type k-log-polyhomogeneous, 17, 106 weight for a trace, 136 weight, conformal, 174 weighted determinant, 157 weighted supertraces, 158 weighted trace, 136 Yamabe operator, 175 Zd-translation invariant, 91 zeta function, 98 zeta regularised traces, 135 zeta-determinant, 168

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