Fractal interpolants on the unit circle Original Research Article

A methodology based on fractal interpolation functions is used in this work to define new real maps on the circle generalizing the classical ones. A partition on the circle and a scale vector enable the modification of the definition and properties of the standard periodic functions. The fractal analogues can be constructed even if the originals are not continuous. The new functions provide Hilbert bases for the square integrable maps on the circle.