Quantitative estimates for singularity for conjugate equations driven by linear fractional transformations

2024/07/16 by Okamura, Kazuki · 1 citation
#26A30 #60G30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.11565

Abstract

We consider the conjugate equation driven by two families of finite maps on the unit interval satisfying a compatibility condition. This framework contains de Rham's functional equations. We give sufficient conditions for singularity of the solution with quantitative estimates in the case that the equation is driven by non-affine maps, in particular, linear fractional transformations.

Cited by

• Dyadic potential theory and de Rham functions

Related

• Dyadic potential theory and de Rham functions
• Detecting discrete integrability: the singularity approach
• Singular solutions of linear problems with fractional Laplacian
• Quantitative regularity for minimizing intrinsic fractional harmonic maps
• Fractional calculus of Weyl algebra and Fuchsian differential equations