Taylor Series in Hermitean Clifford Analysis
نویسندگان
چکیده
منابع مشابه
On primitives and conjugate harmonic pairs in Hermitean Clifford analysis
The notion of a conjugate harmonic pair in the context of Hermitean Clifford analysis is introduced as a pair of specific harmonic functions summing up to a Hermitean monogenic function in an open region Ω of C. Under certain geometric conditions on Ω the conjugate harmonic to a given specific harmonic is explicitly constructed and the potential or primitive of a Hermitean monogenic function is...
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Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator ∂. In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator ∂...
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Clifford analysis offers a higher dimensional function theory studying the null solutions of the rotation invariant, vector valued, first order Dirac operator ∂. In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator ∂J , leading to the system of equations...
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In this note, we describe the Gel’fand-Tsetlin procedure for the construction of an orthogonal basis in spaces of Hermitean monogenic polynomials of a fixed bidegree. The algorithm is based on the Cauchy-Kowalewski extension theorem and the Fischer decomposition in Hermitean Clifford analysis.
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An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way. Utilizing differential algebraic and functional analytic arguments on ...
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ژورنال
عنوان ژورنال: Complex Analysis and Operator Theory
سال: 2009
ISSN: 1661-8254,1661-8262
DOI: 10.1007/s11785-009-0036-y