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Orthogonal polynomials on the product domain [a1,b1]×[a2,b2] with respect to the inner product 〈f,g〉S=∫a1b1∫a2b2∇f(x,y)⋅∇g(x,y)w1(x)w2(y)dxdy+λf(c1,c2)g(c1,c2) are constructed, where wi is a weight function on [ai,bi] for i=1,2, λ>0, and (c1,c2) is a fixed point. The main result shows how an orthogonal basis for such an inner product can be constructed for certain weight functions, in particular,...
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