Szeg$ddot{o}$ projection and matrix Hilbert transform in Hermitean Clifford analysis - Mathematics > Classical Analysis and ODEsReportar como inadecuado




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Abstract: The simultaneous null solutions of the two complex Hermitean Dirac operatorsare focused on in Hermitean Clifford analysis, where the matrix Hilberttransform was presented and proved to satisfy the analogous properties of theHilbert transform in classical analysis and in orthogonal Clifford analysis.Under this setting we will introduce the Szeg$\ddot{o}$ projection operator forthe Hardy space of Hermitean monogenic functions defined on a bounded subdomainof even dimensional Euclidean space, establish the Kerzman-Stein formula whichclosely connects the Szeg$\ddot{o}$ projection operator with the Hardyprojection operator onto the Hardy space of Hermitean monogenic functionsdefined on a bounded subdomain of even dimensional Euclidean space, and get theSzeg$\ddot{o}$ projection operator in terms of the Hardy projection operatorand its adjoint. Further we will give the algebraic and geometriccharacterizations for the matrix Hilbert transform to be unitary in HermiteanClifford analysis.



Autor: Min Ku, Daoshun Wang

Fuente: https://arxiv.org/



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