Corrigendum to: On Harmonic Potential Fields and the Structure of Monogenic Functions, Z. Anal. Anw. 22 (2003)(2), 261-27 (original) (raw)
2006, Zeitschrift für Analysis und ihre Anwendungen
AI-generated Abstract
This corrigendum addresses an error in the original paper regarding the function h_k+1, which was claimed to be the unique R_{0,m}-valued homogeneous polynomial satisfying a specific equation. The correction involves recognizing that h_k+1 does not satisfy the specified equation, but through the Fisher decomposition of homogeneous polynomials, a unique solution can still be established in the revised section of the paper.
Related papers
Harmonic functions associated with some polynomials in several variables
TURKISH JOURNAL OF MATHEMATICS
The aim of this paper is to give various properties of homogeneous operators associated with Chan-Chyan-Srivastava polynomials and, by using these results, to obtain harmonic functions by applying Laplace and ultrahyperbolic operators to the Chan-Chyan-Srivastava polynomials.
On Harmonic Potential Fields and the Structure of Monogenic Functions
Zeitschrift für Analysis und ihre Anwendungen, 2000
In specific open domains of Euclidean space, a correspondence is established between a monogenic function and a sequence of harmonic potential fields, leading to the construction of a unique vector-valued conjugate harmonic homogeneous polynomial to a given real-valued solid harmonic.
On the harmonic and monogenic decomposition of polynomials
Journal of Symbolic Computation, 1989
The decomposition of polynomials in terms of spherical harmonics is widely used in various branches of analysis. In this paper we describe a set of REDUCE procedures generating this decomposition and its more general, monogenic, counterpart in Clifford analysis. We then illustrate their use by inverting the Laplacian and the Dirac operator on both Euclidean and Minkowski spaces.
Planar Harmonic and Monogenic Polynomials of Type A
Symmetry
Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on R N. The Dunkl operators are denoted by T j for 1 ≤ j ≤ N , and the Laplacian ∆ κ = N j=1 T 2 j. This paper finds the homogeneous harmonic polynomials annihilated by all T j for j > 2. The structure constants with respect to the Gaussian and sphere inner products are computed. These harmonic polynomials are used to produce monogenic polynomials, those annihilated by a Dirac-type operator.
Harmonic Polynomials and Dirichlet-Type Problems
Proceedings of The American Mathematical Society, 1995
We take a new approach to harmonic polynomials via differ- entiation. Surprisingly powerful results about harmonic functions can be obtained simply by differentiating the function |x|2−n and observing the patterns that emerge. This is one of our main themes and is the route we take to Theorem 1.7, which leads to a new proof of a harmonic decomposition theorem for
Orthogonal Homogeneous Polynomials
Advances in Applied Mathematics, 1999
An addition formula, Pythagorean identity, and generating function are obtained for orthogonal homogeneous polynomials of several real variables. Application is made to the study of series of such polynomials. Results include an analog of the Funk-Hecke theorem.
Certain Classes of Harmonic Functions Pertaining to Special Functions
Certain classes of harmonic functions pertaining to special functions, Mat. Stud. 36 (2011), 142-151. Making use of generalized Dziok-Srivastava operator we introduced a new class of complexvalued harmonic functions which are orientation preserving, univalent and starlike in the unit disc. We investigate the coefficient bounds, distortion inequalities, extreme points and inclusion results for the generalized class of functions. Г. Муругусундарамурти, К. Виджая, К. Тхилагаватхи. Некоторые классы гармонических функций, касающихся специальных функций // Мат. Студiї. -2011. -Т.36, №2. -C.142-151.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.