OAI/MathematicalPhysics/DefocusingNLS/Linear/HomogeneousSpherePolynomial.lean

GitHub source file

9 declarations, 0 contain sorry, 0 declared as axioms

Polynomial moments separate continuous functions on the physical sphere

Coordinate polynomials are dense by Stone-Weierstrass. This is the first step toward detecting a nonzero spherical harmonic coefficient.

  1. def OAI.DefocusingNLS.physicalSphereCoordinate line 18
  2. def OAI.DefocusingNLS.physicalSpherePolynomial line 21
  3. theorem OAI.DefocusingNLS.physicalSpherePolynomial_X line 25
  4. theorem OAI.DefocusingNLS.physicalSpherePolynomial_apply line 29
  5. theorem OAI.DefocusingNLS.physicalSpherePolynomial_separates line 39
  6. theorem OAI.DefocusingNLS.physicalSpherePolynomial_dense line 51
  7. theorem OAI.DefocusingNLS.physicalSphere_real_eq_zero_of_polynomial_moments line 56
  8. theorem OAI.DefocusingNLS.physicalSphere_eq_zero_of_polynomial_moments line 80
  9. theorem OAI.DefocusingNLS.physicalSphere_exists_polynomial_moment line 108