Martin Lind

collaborators

4 papers

math.CA2026

On the $p$ -variation of Riemann's ''nondifferentiable'' function

Martin Lind

We investigate the variational properties of Riemann's ''nondifferentiable'' function $R$ . We show that $R$ has finite $p$ -variation for $p > 4/3$ and infinite $p$ -variation for $p<4…

math.CA2026

A variation on the PÃ³lya-SegÅ principle in one dimension

Sorina Barza, Martin Lind

We prove a PÃ³lya-SzegÅ principle for the Riesz $(p, I^\pm)$ -variation, a scale of fractional smoothness interpolating between bounded $p$ -variation and the Sobolev space $W^{1, p}$ . I…

math.CA2026

Eliminating positive-measure level sets by small Lipschitz perturbations

Sorina Barza, Martin Lind

We establish a new regularity phenomenon of continuous functions. Specifically, given any continuous function $f$ and arbitrary $I^µ > 0$ , we construct a Lipschitz perturbation $g_{I^} µ$ …

math.CA2026

Fourier transform inequalities, lattice point discrepancy, asymptotic behavior, oscillatory integrals

Martin Lind

For $1 < p \leq 2$ , we establish sharp inequalities for the Fourier transform of the characteristic function of the $l^{p}$ -unit ball $B_{p} \subset R^{2}$ . We show that $$ \sup_{\bol…

On the p-variation of Riemann's ''nondifferentiable'' function

A variation on the PÃ³lya-SegÅ principle in one dimension

Eliminating positive-measure level sets by small Lipschitz perturbations

Fourier transform inequalities, lattice point discrepancy, asymptotic behavior, oscillatory integrals

On the $p$ -variation of Riemann's ''nondifferentiable'' function

A variation on the PÃ³lya-SegÅ principle in one dimension