4 problems

For $b\in\mathbb{N}$, $0<\alpha<1$, and a $\mathbb{Z}$-periodic Lipschitz function $g$, let … and denote the corresponding family of Weierstrass-type functions by…

Let $k$ be a positive integer, partition the range $[0,1]$ uniformly into $k$ pieces, and choose an appropriate piecewise linear base function. Uniform-partition extension conjectu…

Basic conjecture. For any function from the Hölder class given by its discrete values, one can specify a sample size $N$ such that there is an interval $[\alpha,\beta]$ on which

Discrete-grid complexity conjecture. For Hölder-class functions, the following equality should hold: