# On one set of orthogonal harmonic polynomials

@inproceedings{Karachik1998OnOS, title={On one set of orthogonal harmonic polynomials}, author={V. Karachik}, year={1998} }

A new basis of harmonic polynomials is given. Proposed polynomials are orthogonal on the unit sphere and each term of this basis consists of monomials not present in the others. Introduction For the investigation of harmonic polynomials a scalar product for homogeneous polynomials of degree m in the form 〈Pm(x), Qm(x)〉 = Pm(D)Qm(x) was introduced in [1]—one of the basic works on harmonic analysis— where the operator Pm(D) is obtained from the polynomial Pm(x) by replacing each variable xi on… Expand

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