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