A boundedness criterion for the variations of self-similar functions
The authors study regularity properties of self-similar functions. They provide conditions on such functions ensuring either continuity or finiteness of the total variation (e.g., membership in the class \(BV\)). The criteria for membership in \(BV\) are more complicated for continuous functions than for discontinuous functions. As an application, the authors discuss a spectral problem associated to the eigenvalue counting function of a certain boundary value ODE.
scientific article; zbMATH DE number 6032833