Discrete Hardy spaces. (English) Zbl 1308.44002
The authors summarize the contents of this paper in the abstract as follows: We study the boundary behavior of discrete monogenic functions, i.e. null-solutions of a discrete Dirac operator, in the upper and lower half space. Calculating the Fourier symbol of the boundary operator we construct the corresponding discrete Hilbert transforms, the projection operators arising from them, and discuss the notion of discrete Hardy spaces. Hereby, we focus on the 3D-case with the generalization to the \(n\)-dimensional case being straightforward.
Reviewer: Kun Soo Chang (Seoul)
MSC:
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 65T50 | Numerical methods for discrete and fast Fourier transforms |
Keywords:
discrete Dirac operator; discrete Cauchy transform; discrete monogenic functions; Hardy space; Fourier symbol; discrete Hilbert transformReferences:
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