Discrete pseudo‐differential operators in hypercomplex analysis

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...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 47; no. 10; pp. 8025 - 8041
Main Authors: Cerejeiras, Paula, Kaehler, Uwe, Lucas, Simão
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 15.07.2024
Subjects:
Differential equations
discrete Dirac operators
discrete symbols
functions of hypercomplex variables and generalized variables
Operators (mathematics)
pseudodifferential operators
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary: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.
Bibliography:Dedicated to K. Gürlebeck on the occasion of his 65th birthday.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7881