Abstract
As an integral part of a pseudodifferential calculus for boundary value problems on manifolds with edges we introduce the algebra of Mellin operators. They represent the typical operators near the edge. In fact we show how to associate an operator-valued Mellin symbol to an arbitrary edge-degenerate pseudodifferential boundary value problem, the so-called ‘Mellin quantization’ procedure. Furthermore, we introduce a class of adequate Sobolev spaces based on the Mellin transform on which these operators act continuously.
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Schrohe, E., Schulze, BW. (1998). Mellin operators in a pseudodifferential calculus for boundary value problems on manifolds with edges. In: Gohberg, I., Mennicken, R., Tretter, C. (eds) Differential and Integral Operators. Operator Theory: Advances and Applications, vol 102. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8789-2_19
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DOI: https://doi.org/10.1007/978-3-0348-8789-2_19
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