A Dirichlet Problem for the First Order Inhomogeneous Meta-Monogenic Equation in Parameter Depending Clifford Algebras

Teodoro, Antonio Di; Vanegas, Judith

doi:10.1007/s11785-014-0390-2

Cited by 2 publications

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“…These operators are discrete analogues of continuous Dirac operators with non-constant coefficients which have been studied in the literature, e.g., in literature. [23][24][25] A particular important example of such operators is the Beltrami equation. 26 Here, we can clearly see the advantages of the discrete pseudo-differential calculus.…”

Section: Conflict Of Interestmentioning

confidence: 99%

“…Let us now take a look at the Dirac operator with non‐constant coefficients, i.e.,

D_{h}^{+ -} = \sum_{j = 1}^{n} e_{j}^{+} a_{j}^{+} (x) \partial_{h}^{+ j} + e_{j}^{-} a_{j}^{-} (x) \partial_{h}^{- j} .

These operators are discrete analogues of continuous Dirac operators with non‐constant coefficients which have been studied in the literature, e.g., in literature 23–25 . A particular important example of such operators is the Beltrami equation 26 …”

Section: Examples Of Discrete Symbols Of Discrete Operatorsmentioning

confidence: 99%

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Discrete pseudo‐differential operators in hypercomplex analysis

Cerejeiras

Kähler

Lucas

2021

Math Methods in App Sciences

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In this paper we discuss discrete pseudo‐differential operators in the context of hypercomplex analysis. We will provide the definitions and establish the necessary calculus which will be used to discuss questions like boundedness and compactness of operators. In the end, we will discuss well‐known examples from hypercomplex analysis as well as give new examples including discrete Dirac operators with non‐constant coefficients.

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