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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	The index of quantized contact transformations on manifolds with conical singularities Schulze, Bert-Wolfgang, Nazaikinskii, Vladimir, Sternin, Boris January 1998 (has links) The quantization of contact transformations of the cosphere bundle over a manifold with conical singularities is described. The index of Fredholm operators given by this quantization is calculated. The answer is given in terms of the Epstein-Melrose contact degree and the conormal symbol of the corresponding operator. manifolds with conical singularities contact transformations quantization ellipticity Fredholm operators regularizers index formulas Mathematics