Title: Regularised integrals, sums, and traces : an analytic point of view /
Authors: Paycha, Sylvie.
Publisher: American Mathematical Society,
Year: 2012
Subjects: Operator theory -- Linear spaces and algebras of operators -- Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.); Functions, Zeta.; L-functions.; Convergence.; Integrals.; Number theory -- Zeta and $L$-functions: analytic theory -- $\zeta (s)$ and $L(s, \chi)$.; Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of integrals.; Quantum theory -- Quantum field theory; related classical field theories -- Anomalies.; Numerical analysis -- Acceleration of convergence -- Euler-Maclaurin formula.
Contents: Gamma function extended to nonpositive integer points -- Canonical integral and noncommunicative residue on symbols -- Cut-off regularised integral -- Noncommutative residue as a complex residue -- Canonical sum on noninteger order classical symbols -- Traces on pseudodifferential operators -- Weighted traces -- Logarithmic residues -- Anomalies of regularised determinants.