Abstract
We consider a commutative algebra B over the field of complex numbers with a basis {e 1, e 2} satisfying the conditions \((e_1^2+e_2^2)^2=0\), \(e_1^2+e_2^2\ne 0\). We consider a Schwarz-type boundary value problem for “analytic” B-valued functions in a simply connected domain. This problem is associated with BVPs for biharmonic functions. Using a hypercomplex analog of the Cauchy type integral, we reduce these BVPs to a system of integral equations on the real axes. We establish sufficient conditions under which this system has the Fredholm property.
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Gryshchuk, S.V., Plaksa, S.A. (2019). Biharmonic Monogenic Functions and Biharmonic Boundary Value Problems. In: Lindahl, K., Lindström, T., Rodino, L., Toft, J., Wahlberg, P. (eds) Analysis, Probability, Applications, and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04459-6_14
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