Abstract
The pseudo-differential calculus on a manifold with conical singularities extends in a natural way to spaces of hedgehog shape, e.g., to manifolds that are transversally intersected by intervals. For treating the higher-dimensional analogues for spaces with components of different dimensions it is nessecary to establish a corresponding theory in the framework of an algebra which is the range of operator-valued symbols in the Fourier-edge approach. The present paper constructs such an algebra on hedgehog configurations, based on Mellin pseudo-differential operators, acting in weighted Sobolev spaces with (and without) asymptotics. We introduce ellipticity, obtain Fredholm operators and parametrix constructions within the algebras. The elliptic regularity of solutions will be formulated with (and without) asymptotics in the weighted Mellin Sobolev spaces.
AMS Subject Classification: 35 S 05, 35 J 70, 58 G 15.
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© 1995 Birkhäuser Verlag Basel/Switzerland
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Schulze, BW. (1995). Transmission Algebras on Singular Spaces With Components of Different Dimensions. In: Demuth, M., Schulze, BW. (eds) Partial Differential Operators and Mathematical Physics. Operator Theory Advances and Applications, vol 78. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9092-2_35
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DOI: https://doi.org/10.1007/978-3-0348-9092-2_35
Publisher Name: Birkhäuser Basel
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