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On a modification of the Poisson integral operator

Dariusz Partyka (2011)

Annales UMCS, Mathematica

Given a quasisymmetric automorphism γ of the unit circle T we define and study a modification Pγ of the classical Poisson integral operator in the case of the unit disk D. The modification is done by means of the generalized Fourier coefficients of γ. For a Lebesgue's integrable complex-valued function f on T, Pγ[f] is a complex-valued harmonic function in D and it coincides with the classical Poisson integral of f provided γ is the identity mapping on T. Our considerations are motivated by the...

On a noncommutative algebraic geometry

(2015)

Banach Center Publications

Several sets of quaternionic functions are described and studied with respect to hyperholomorphy, addition and (non-commutative) multiplication, on open sets of ℍ, then Hamilton 4-manifolds analogous to Riemann surfaces, for ℍ instead of ℂ, are defined, and so begin to describe a class of four-dimensional manifolds.

On a paper of Carleson.

Brakalova, Melkana A., Jenkins, James A. (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

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