Using periodic Strang--Fix conditions, we can give an approach to error estimates for periodic interpolation on equidistant and sparse grids for functions from certain Besov spaces.

Interpolation (msc 41A05), Multidimensional problems (should also be assigned at least one other classification number in this section) (msc 41A63), Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems (msc 46E35), Interpolation (msc 65D05)
Modelling, Analysis and Simulation [MAS]

Sickel, W, & Sprengel, F. (1998). Some error estimates for periodic interpolation of functions from Besov spaces. Modelling, Analysis and Simulation [MAS]. CWI.