Index

admissible operator, 131

admissible set of operators, 142

admissible set of symbols, 26

Bernoulli numbers, 79

Bernoulli polynomials, 80

Beta function, 3

bidegree of conformal covariance, 174

canonical discrete sum, 94

canonical integral, 28

canonical trace, 123

classical symbol on an open set, 106

closed linear forms, 22

conformal anomaly, 180

conformal Laplacian, 175

conformality, 174

conformally covariant operators, 174

conformally invariant functional, 177

continuity of a weighted trace, 148

continuity of the residue, 122

convex (closed) polytope, 83

covariant linear forms on symbols, 32

covariant set of symbols, 32

cut-off Gamma function, 11

cut-off integral, 36, 86

cut-off sum, 82, 89

defect formula, 148

dimensional regularisation, 72

discrepancies, 12, 13, 39, 74, 139

elliptic operator, 111

energy-momentum tensor, 181

Epstein’s ζ-function, 102

Euler’s constant, 2

Euler’s lemma, 21

Euler-Maclaurin formula, 80, 81

excision function around the origin, 17

expanded polytope, 84

formal classical symbols, 19

Fr´ echet topology on classical operators, 117

Fr´ echet topology on classical symbols, 19

Gamma function, 2

Hadamard integral and method, 7, 36

Hadamard extension of Gamma, 11

Hadamard finite part method, 1, 7

heat-kernel regularised trace, 158

holomorphic regularisation on operators,

135

holomorphic family in a Banach space, 56

holomorphic family of operators, 56, 133

holomorphic family of symbols, 57

holomorphic regularisation on symbols, 70

homogeneous distribution, 2, 16

Hurwitz zeta function, 98

index of D+, 159

integral polytopes, 83

kernel of an operator, 108

Khovanskii-Pukhlikov formula, 84

Laplace-Beltrami operator, 162, 175

leading symbol, 18, 107, 111, 116

Lichnerowicz formula, 162

local conformal anomaly, 181

local discrepancies, 139

localisation subordinated to a chart, 114

locality of the noncommutative residue, 119

log-polyhomogeneous operator, 111

log-polyhomogeneous order, 107

log-polyhomogeneous symbol, 17, 107

log-type, 17, 107

minimal subtraction scheme, 54

modified dimensional regularisation, 70

multiplicative anomaly of a weighted

determinant, 170

multiplicative anomaly of the zeta

determinant, 173

noncommutative residue of a symbol, 21

noncommutative residue of an operator,

121

nonlocality of canonical traces, 123

nonlocality of regularised traces, 136

189