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- W2520226503 abstract "The $$Pi $$ -operator (Ahlfors–Beurling transform) plays an important role in solving the Beltrami equation. In this paper we define two $$Pi $$ -operators on the n-sphere. The first spherical $$Pi $$ -operator is shown to be an $$L^2$$ isometry up to isomorphism. To improve this, with the help of the spectrum of the spherical Dirac operator, the second spherical $$Pi $$ operator is constructed as an isometric $$L^2$$ operator over the sphere. Some analogous properties for both $$Pi $$ -operators are also developed. We also study the applications of both spherical $$Pi $$ -operators to the solution of the spherical Beltrami equations." @default.
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- W2520226503 date "2017-02-09" @default.
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- W2520226503 title "Spherical $$Pi $$ Π -Type Operators in Clifford Analysis and Applications" @default.
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- W2520226503 doi "https://doi.org/10.1007/s11785-017-0641-0" @default.
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