Nonlinear singular integral equations involving the Hilbert transform in Clifford analysis (Q1301258)
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scientific article; zbMATH DE number 1331705
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear singular integral equations involving the Hilbert transform in Clifford analysis |
scientific article; zbMATH DE number 1331705 |
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Nonlinear singular integral equations involving the Hilbert transform in Clifford analysis (English)
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16 July 2000
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The author is working in the Clifford algebra \(C\ell_{n,0}\) (with \(e_j^2 = +1\)), after introducing the necessary definitions especially those of Teodorescu and Cauchy type operators some properties of these are proved. Then the Hilbert transform \(H\) is defined and investigated together with its relation to the Cauchy-Fueter differential operator \( D = \sum_{i=1}^ne_i\frac{\partial} {\partial x_j}.\) Results for the Nemytskij operator follow. The last chapter deals with monotonicity principles for integral operators, namely with Hammerstein-type equations, maximal monotone operators, and integro-differential equations.
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Clifford analysis
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Cauchy type transform
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Hilbert transform
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Nemytskij operator
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monotone integral operators
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