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This memoir is a study of Ray-Singer analytic torsion for hermitian vector bundles on a compact Riemann surface [italic]C. The torsion is expressed through the trace of a modified resolvent. Thus, one can develop perturbation-curvature formulae for the Green-Szegö kernel and al…
The purpose of this memoir is twofold: to extend the notions of kernel and integral operator to the context of continuous sums of Banach spaces; and to extend to this setting, certain well-known conditions for an integral operator to be compact, Hilbert-Schmidt and trace-class.
