Singular integral operators on Riemann surfaces and elliptic differential systems |
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Authors: | Yu L Rodin |
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Institution: | (1) Department of Mathematics, Wayne State University, 48202-9861 Detroit, MI |
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Abstract: | The derivatives of the Cauchy kernels on compact Riemann surfaces generate singular integral operators analogous to the Calderón-Zigmund
operators with the kernel (t - z)2 on the complex plane. These operators play an important role in studying elliptic differential equations, boundary value
problems, etc. We consider here the most important case of the multi-valued Cauchy kernel with real normalization of periods.
In the opposite plane case, such an operator is not unitary. Nevertheless, its norm in L2 is equal to one. This result is used to study multi-valued solutions of elliptic differential systems. |
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Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 30F30 |
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