Try using Circle OPs for quartic OPs

[dlfivefifty]

An idea occurred to me: Let P(x,y) be a family of OPs on the circle w.r.t. w(x) and Q(x,y) w.r.t to sqrt(1-x^2)*w. Let y = (1-x^2)^(1/4). Then can't we write quartic OPs in terms of P(x,y^2) and y*Q(x,y^2)?

[dlfivefifty]

@MarcoFasondini

[MarcoFasondini]

I don't see how this can be done:

[dlfivefifty]

We only need orthogonality w.r.t. lower degree polynomials (then the true OPs lie in the span of the set).