Tchebycheff approximation of continuous functions by harmonic polynomials on conic sections

AbstractThe problem of finding a best Tchebycheff approximation to a given continuous function f, defined on a compact portion of a plane conic section, from the set of harmonic polynomials of degree n or less is studied. It is shown that the Haar condition is fulfilled by such harmonic polynomials. Interesting relationships which exist between this problem and certain classical approximation problems are explored. Numerical examples are given to illustrate the theory