Abstract
The Duduchava–Roch formula is a formula for the inverse of a Toeplitz matrix that is generated by a pure Fisher–Hartwig singularity. We cite this formula with a full proof and give several of its applications. These are the Fredholm theory of Toeplitz operators with piecewise continuous symbols, the derivation of the pure Fisher–Hartwig determinant, problems connected with lattice determinants, and Green’s function for a boundary value problem for a higher-order ordinary differential operator.
For Roland Duduchava on his 70th birthday
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Böttcher, A. (2017). The Duduchava–Roch Formula. In: Maz'ya, V., Natroshvili, D., Shargorodsky, E., Wendland, W. (eds) Recent Trends in Operator Theory and Partial Differential Equations. Operator Theory: Advances and Applications, vol 258. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-47079-5_1
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DOI: https://doi.org/10.1007/978-3-319-47079-5_1
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-47077-1
Online ISBN: 978-3-319-47079-5
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