130 INDEX numerical , 41 Index theorem L2-index theorem, 98, 101 Atiyah-Singer formula, 97, 98 Injectivity radius, 90 Isolated spectral dimension, 56 Jordan decomposition, 10, 16 Kasparov module, 35 local index formula, 83 McKean-Singer, 85 Moyal plane, 110 Projective tensor product, 11 Pseudodifferential operators, 22 regular, 22 tame, 22 Taylor expansion, 26 Residue cocycle, 57 Resolvent cocycle, 58 φr m defined using resolvent function Rs(λ), 58 φr m,t defined using resolvent function Rs,t(λ), 58 Resolvent function, 30, 57 Rs(λ) = (λ − (1 + s2 + D2))−1, 57 Rs,t,u(λ) = (λ − (t + s2 + D2))−1, u 57 Rs,t(λ) = (λ − (t + s2 + D2))−1, 57 Schatten ideals, 9 Schatten norm estimates, 29 Semifinite Fredholm module, 37 finitely summable, 37 pre-Fredholm module, 37 Semifinite spectral triple, 34 QC∞, 45 QCk, 45 QCk summable, 46 δ-ϕ-topology, 46 δ-topology, 45 discrete dimension spectrum, 56 finitely summable, 43 isolated spectral dimension, 56 smoothly summable, 46 spectral dimension, 43 Seminorms, 8 Pn, seminorms on B1(D, p), 13, 14 Pn,l, seminorms on Bk(D, 1 p), B∞(D, 1 p), 21 Pr n,l , seminorms on OPr, 0 22 Qn, seminorms on B2(D, p), 8 Spectral dimension, 43 Torus actions, 103 Transgression cochain, 58 BΦr M+1,0,u defined using resolvent function Rs,0,u(λ), 58 Φr m,t defined using resolvent function Rs,t(λ), 58 Φr m defined using resolvent function Rs(λ), 58 Weyl pseudodifferential calculus, 111 Zeta function, 56

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