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1	On the index of differential operators on manifolds with conical singularities Schulze, Bert-Wolfgang, Sternin, Boris, Shatalov, Victor January 1997 (has links) The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point. conical singularities Mellin transform pseudodiferential operators ellipticity Fredholm operators regularizers analytic index Mathematics
2	A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators Schulze, Bert-Wolfgang, Nazaikinskii, Vladimir, Sternin, Boris January 1998 (has links) For general endomorphisms of elliptic complexes on manifolds with conical singularities, the semiclassical asymptotics of the Atiyah-Bott-Lefschetz number is calculated in terms of fixed points of the corresponding canonical transformation of the symplectic space. elliptic operator Fredholm property conical singularities pseudodiferential operators Lefschetz fixed point formula regularizer Mathematics