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JuliaApproximation / MultivariateOrthogonalPolynomials.jl

Supports approximating functions and solving differential equations on various higher dimensional domains such as disks and triangles
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New Operator: AngularMomentum #81

Open MikaelSlevinsky opened 3 years ago

MikaelSlevinsky commented 3 years ago

This one is just about as fundamental as the Laplacian. For complex spherical harmonics and Zernike polynomials, it's diagonal. Other multivariate OPs may have nontrivial representations. In polar coordinates, it's ∂/∂θ; in spherical coordinates, it's ∂/∂φ. Or in both systems, it's x ∂/∂y - y ∂/∂x. Since it's spectrum "separates orders," it is complementary to the Laplacian which "separates degrees."

dlfivefifty commented 3 years ago

What would you call r ∂/∂r = x ∂/∂x + y ∂/∂y?

MikaelSlevinsky commented 3 years ago

I don't know, a Cauchy-Euler operator? https://en.m.wikipedia.org/wiki/Cauchy–Euler_operator

A Homogeneous operator? https://mathworld.wolfram.com/EulersHomogeneousFunctionTheorem.html