Discrete Hardy Spaces
Copyright policy )Discrete Hardy Spaces
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.
- University of Aveiro Portugal
- University of Aveiro (UAVR) Portugal
- Ghent University Belgium
- UNIVERSIDADE DE AVEIRO Portugal
- University of Aveiro Portugal
Fourier symbol, discrete Cauchy transform, CLIFFORD ANALYSIS, discrete Dirac operator, discrete monogenic functions, Hardy space, discrete Hilbert transform, Discrete monogenic functions, DIRAC OPERATORS, Discrete Cauchy transform, Dirac Operators, Mathematics and Statistics, Discrete Dirac operator, Clifford Analysis, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Special integral transforms (Legendre, Hilbert, etc.), Numerical methods for discrete and fast Fourier transforms
Fourier symbol, discrete Cauchy transform, CLIFFORD ANALYSIS, discrete Dirac operator, discrete monogenic functions, Hardy space, discrete Hilbert transform, Discrete monogenic functions, DIRAC OPERATORS, Discrete Cauchy transform, Dirac Operators, Mathematics and Statistics, Discrete Dirac operator, Clifford Analysis, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Special integral transforms (Legendre, Hilbert, etc.), Numerical methods for discrete and fast Fourier transforms
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