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Try using Circle OPs for quartic OPs #2

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dlfivefifty opened this issue Sep 22, 2020 · 3 comments
Open

Try using Circle OPs for quartic OPs #2

dlfivefifty opened this issue Sep 22, 2020 · 3 comments

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@dlfivefifty
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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
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@MarcoFasondini

@MarcoFasondini
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I don't see how this can be done:
4th_deg_OPs

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

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@dlfivefifty @MarcoFasondini