Abstract

A family of orthonormal polynomials on the unit ball B d of R d with respect to the inner product 〈 f , g 〉 = ∫ B d Δ [ ( 1 - ∥ x ∥ 2 ) f ( x ) ] Δ [ ( 1 - ∥ x ∥ 2 ) g ( x ) ] dx , where Δ is the Laplace operator, is constructed explicitly.

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