Local spline approximation of discontinuous functions and location of discontinuities, given low-order Fourier coefficient information. (Q1426817)

Local and robust approximations functions by spline projections are studied in this paper. The functions are represented by low index Fourier coefficients. A special emphasis is given to the localness of the methods, i.e. that the global behaviour of the function should have little influence on the approximation on a subinterval. The function is allowed to have discontinuities that are to be located by the method.