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An inverse for the Gohberg-Krupnik symbol map

  • Martin Costabel (a1)

Synopsis

It is shown that the elements of the closed operator algebra generated by one-dimensional singular integral operators with piecewise continuous coefficients with a fixed finite set of points of discontinuity can be written as the sum of a singular integral operator, a compact operator, and generalized Mellin convolutions. Their Gohberg-Krupnik symbol is given in terms of the Mellin transform. This gives an explicit construction of an operator with prescribed Gohberg—Krupnik symbol.

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An inverse for the Gohberg-Krupnik symbol map

  • Martin Costabel (a1)

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