A Paley-Wiener theorem and Wiener-Hopf-type integral equations in Clifford analysis
Some convolution-type integral equations over the real line can be treated efficiently by reducing them to the Hilbert (=Riemann) boundary value problems for holomorphic functions in one complex variable. The author extends the idea onto the multidimensional situation by establishing relations between the Wiener-Hopf-type integral equations and boundary values of monogenic (= hyperholomorphic = regular) functions of Clifford analysis. A Paley-Wiener theorem for such functions is proved, as well as a hypercomplex analog of the Krein factorization theorem.
scientific article; zbMATH DE number 1240577
scientific article