22.—Analytic, Generalized, Hyperanalytic Function Theory and an Application to Elasticity
- 1 January 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 73, 317-331
- https://doi.org/10.1017/s0308210500016474
Abstract
Synopsis: Though it is still an open problem for which class of first-order elliptic systems Carleman's theorem holds, this is proven here for a certain class of systems (with analytic coefficients) for which Douglis introduced the hypercomplex algebra and hyperanalytic functions. The proof is based on a representation formula generalising Vekua's approach with Volterra integral equations in C2 to more than two unknowns. The representation formula is of its own interest because it provides the generation of complete families of solutions. The equations of plane inhomogeneous elasticity problems lead to a system of the desired class.Keywords
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