Complexity of local solution of multivariate integral equations (Q1908041)

The complexity of a local solution of Fredholm integral equations of the second kind for a Sobolev class of multivariate periodic functions with dominating mixed derivative is discussed. To prove the lower bound, an \(s\)-number technique is used, which was applied earlier to two other special classes of functions. The upper bound is proved in a constructive way providing an implementable algorithm of optimal order based on Fourier coefficients and a hyperbolic cross approximation.