Orthogonal expansions for generalized Gegenbauer weight function on the unit ball

الأصل · EN

Orthogonal polynomials and expansions are studied for the weight function hκ²(x) x²ν (1-x²)μ⁻¹/² on the unit ball of Rᵈ, where hκ is a reflection invariant function, and for related weight function on the simplex of Rᵈ. A concise formula for the reproducing kernels of orthogonal subspaces is derived and used to study summability of the Fourier orthogonal expansions.