Abstract
The \(\bar \partial\)-problem in complex analysis has stimulated deep and fruitful investigations. Since two-dimensional complex analysis can be embedded into one dimensional quaternionic analysis, one expects that the study of the analogous problem ψ D[u] = α in a domain Ω ⊂ H = quaternions, for fixed parameter ψ ∈ H 4, will be useful and promising. We establish some basic facts concerning operators on quaternionic Hilbert modules, and establish connections among the hyperholomorphic Bergman projector, the so-called T-operator, and a special solution of the ψ D equation.
This work was partially supported by CONACYT project 1821-E9211
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© 1993 Kluwer Academic Publishers
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Porter, R.M., Shapiro, M.V., Vasilevski, N.L. (1993). On the Analogue of the \(\bar \partial\)-Problem in Quaternionic Analysis. In: Brackx, F., Delanghe, R., Serras, H. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 55. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2006-7_20
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DOI: https://doi.org/10.1007/978-94-011-2006-7_20
Publisher Name: Springer, Dordrecht
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