Uniform Approximation of Geophysical Fields on a Sphere by Trigonometric Polynomials

摘要

The spherical (geographical) coordinate system, which is an analog of Cartesian coordinates on a' sphere, is widely used in the solution of geophysical problems. Any continuous function of a real variable (geophysical field) can be approximated to any arbitrary accuracy along latitudinal circles by a trigonometric polynomial. The functions in the spherical coordinate system are denned along the meridian over segment [0, π]. These functions can be approximated by series of Legendre polynomials or Chebyshev polynomials of the first kind (even functions) and Chebyshev polynomials of the second kind (odd functions).