Abstract
Using finite differences, discrete analogues of the Cauchy-Riemann operator in the complex case can be described in form of 2 x 2 matrix operators. By the help of the discrete Fourier transform the fundamental solution of these difference operators is calculated. The approximation error of the fun-damental solution can be estimated in the space l p as well as in the space L p .
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Gürlebeck, K., Hommel, A. (2003). Finite Difference Cauchy-Riemann Operators and Their Fundamental Solutions in the Complex Case. In: Böttcher, A., Kaashoek, M.A., Lebre, A.B., dos Santos, A.F., Speck, FO. (eds) Singular Integral Operators, Factorization and Applications. Operator Theory: Advances and Applications, vol 142. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8007-7_6
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DOI: https://doi.org/10.1007/978-3-0348-8007-7_6
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