Walsh and wavelet methods for differential equations on the Cantor group
Elena Alexandrovna Lebedeva, M. Skopina · arXiv (Cornell University) · 2014
Ordinary and partial differential equation for unknown functions defined on the Cantor dyadic group are studied. We consider two types of equations: related to the Gibbs derivatives and to the fractional modified Gibbs derivatives (or pseudo differential-operators). We find solutions in classes of distributions and study under what assumptions these solutions are regular functions with some "good" properties.