Details

Autor(en) / Beteiligte

• Xu, Yuan

Titel

Orthogonal Polynomials and Fourier Orthogonal Series on a Cone

Ist Teil von

• The Journal of fourier analysis and applications, 2020-06, Vol.26 (3), Article 36

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Orthogonal polynomials and the Fourier orthogonal series on a cone in R d + 1 are studied. It is shown that orthogonal polynomials with respect to the weight function ( 1 - t ) γ ( t 2 - ‖ x ‖ 2 ) μ - 1 2 on the cone V d + 1 = { ( x , t ) : ‖ x ‖ ≤ t ≤ 1 } are eigenfunctions of a second order differential operator, with eigenvalues depending only on the degree of the polynomials, and the reproducing kernels of these polynomials satisfy a closed formula that has a one-dimensional characteristic. The latter leads to a convolution structure on the cone, which is then utilized to study the Fourier orthogonal series. This narrative also holds, in part, for more general classes of weight functions. Furthermore, analogous results are also established for orthogonal structure on the surface of the cone.