A Paley-Wiener theorem and Wiener-Hopf-type integral equations in Clifford analysis
Copyright policy )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.
Riemann boundary value problems, Wiener-Hopf type integral equations, Hilbert problem, Functions of hypercomplex variables and generalized variables, Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Boundary value problems in the complex plane, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), Paley-Wiener theorem, Krein factorization, convolution-type integral equations, Clifford analysis
Riemann boundary value problems, Wiener-Hopf type integral equations, Hilbert problem, Functions of hypercomplex variables and generalized variables, Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Boundary value problems in the complex plane, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), Paley-Wiener theorem, Krein factorization, convolution-type integral equations, Clifford analysis
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