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
Previous Page Next Page