Abstract
Starting with classical convolutional integral equations on ℝn, translation-invariant operators and their symbol representation according to Hörmander are introduced. The various generalizations concerning the domains G of integration lead to Wiener-Hopf integral and integro-differential equations on ℝ n+ and on cones. Compound integral and integro-differential equations of the principal value and L1-kernel type are discussed on ℝn using results by Rakovshčik. Simonenko's theory of local type operators permits us to investigate generalized translation invariant operators. Wiener-Hopf integral equations with strongly singular kernels correspond to equations with piecewise continuous symbols in both variables. Convolutional equations on quadrants and wedges are studied via the theorey of operators of bi-local type.
Keywords
- Toeplitz Operator
- Singular Integral Equation
- Singular Integral Operator
- Riemann Boundary
- Translation Invariant Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Extended version of a General Lecture at the Dundee Conference on Differential Equations, 31st March 1978.
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Meister, E. (1980). Some classes of integral and integro-differential equations of convolutional type. In: Everitt, W.N. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091381
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