Martin Lind

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20122026

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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 Pólya-Segő principle in one dimension

Sorina Barza, Martin Lind

We establish a one-dimensional Pólya-Szegő principle for the Riesz $(p, α)$ -variation $V_{p}^{α}$ , a family of functionals that interpolates between Wiener $p$ -variation and t…

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 $ε > 0$ , we construct a Lipschitz perturbation $g_{ε}$ w…

math.CA2015

Nonlinear nonnested 2-D spline approximation

Martin Lind, Pencho Petrushev

Nonlinear approximation from regular piecewise polynomials (splines) of degree $< k$ supported on rings in $R^{2}$ is studied. By definition a ring is a set in $R^{2}$ obtained by sub…

math.CA2012

On embeddings of spaces of bivariate functions of bounded $p$ -variation

Martin Lind

We obtain sharp estimates of the Hardy-Vitali type total $p$ -variation of a function of two variables in terms of its mixed modulus of continuity in $L^{p} ([0, 1]^{2})$ . We also investi…

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

A variation on the Pólya-Segő principle in one dimension

Eliminating positive-measure level sets by small Lipschitz perturbations

Nonlinear nonnested 2-D spline approximation

On embeddings of spaces of bivariate functions of bounded p-variation

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

On embeddings of spaces of bivariate functions of bounded $p$ -variation