Martin Lind

Martin Lind
Karlstads Universitet · Department of Mathematics and Computer Science

Ph.D.

About

22
Publications
1,303
Reads
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50
Citations
Additional affiliations
August 2014 - June 2015
University of South Carolina
Position
  • Visiting Assistant Professor
August 2013 - present
Karlstads Universitet
Position
  • Professor (Assistant)
September 2008 - June 2013
Karlstads Universitet
Position
  • PhD Student

Publications

Publications (22)
Preprint
Full-text available
We re-examine through an example the connection between the curvature of the boundary of a set, and the decay at infinity of the Fourier transform of its characteristic function. Let $B_p\subset\mathbb{R}^2$ denote the unit ball of $\mathbb{R}^2$ in the $l^p$-norm. It is a consequence of a classical result of Hlawka that for each $p\in(1,2]$, there...
Article
Full-text available
Let $\nu$ be a nondecreasing concave sequence of positive real numbers and $1\leq p<\infty$. In this note, we introduce the notion of modulus of $p$-variation for a function of a real variable, and show that it serves in at least two important problems, namely, the uniform convergence of Fourier series and computation of certain $K$-functionals. Us...
Article
We consider an equidistributed concatenation sequence of pseudorandom rational numbers generated from the primes by an inversive congruential method. In particular, we determine the sharp convergence rate for the star discrepancy of said sequence. Our arguments are based on well-known discrepancy estimates for inversive congruential pseudorandom nu...
Preprint
Full-text available
We consider a certain equidistributed sequence of rational numbers constructed from the primes. In particular, we determine the sharp convergence rate for the star discrepancy of said sequence. Our arguments are based on well-known discrepancy estimates for inversive congruential pseudorandom numbers together with asymptotic formulae involving prim...
Preprint
Full-text available
In this note, we introduce the notion of modulus of $p$-variation for a function of a real variable, and show that it serves in at least two important problems, namely, the uniform convergence of Fourier series and computation of certain $K$-functionals. To be more specific, let $\nu$ be a nondecreasing concave sequence of positive real numbers and...
Article
Full-text available
In this paper, we study the numerical approximation of a coupled system of elliptic–parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an unsaturated heterogeneous medium with distributed microstructures as they often arise in modeling reactive flow...
Preprint
Full-text available
When applying the quasi-Monte Carlo (QMC) method of numerical integration, Koksma's inequality provides a basic estimate of the error in terms of the discrepancy of the used evaluation points and the total variation of the integrated function. We present an improvement of Koksma's inequality that is also applicable for functions with infinite total...
Article
Full-text available
We develop and implement a numerical model to simulate the effect of photocatalytic asphalt on reducing the concentration of nitrogen monoxide (NO) due to the presence of heavy traffic in an urban environment. The contributions in this paper are threefold: we model and simulate the spread and breakdown of pollution in an urban environment, we provi...
Preprint
We develop and implement a numerical model to simulate the effect of photovoltaic asphalt on reducing the concentration of nitrogen monoxide due to the presence of heavy traffic in an urban environment. The contributions in this paper are threefold: we model and simulate the spread and breakdown of pollution in an urban environment, we provide a pa...
Preprint
Full-text available
In this paper, we study the evolution of a gas-liquid mixture via a coupled system of elliptic-parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an unsaturated heterogeneous medium with distributed microstructures. Besides ensuring the well-posednes...
Article
Full-text available
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 subtracting a compact convex set with polygonal boundary from another such a set, but without creating uncontrollably narrow elongated subregions. Nested structure of the ri...
Article
We establish the well-posedness of a coupled micro-macro parabolic-elliptic system modeling the interplay between two pressures in a gas-liquid mixture close to equilibrium that is filling a porous media with distributed microstructures. Additionally, we prove a local stability estimate for the inverse micro-macro Robin problem, potentially useful...
Article
We study the multiscale approximation of a reaction-diffusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done via micro-macro flux conditions. Our target system has a typical structure for reaction-diffusion-flow problems in media with distributed microstructures (also called, double porosity m...
Article
Full-text available
We obtain a new variational characterization of the Sobolev space \(W_p^1(\Omega )\) (where \(\Omega \subseteq \mathbb {R}^n\) and \(p>n\) ). This is a generalization of a classical result of F. Riesz. We also consider some related results.
Article
We investigate Fubini-type properties of the space of functions of bounded Hardy-Vitali-type p-variation. This leads us to consider mixed norm spaces of bivariate functions whose linear sections have bounded p-variation in the sense of Wiener.
Thesis
Full-text available
The classical concept of the total variation of a function has been extended in several directions. Such extensions find many applications in different areas of mathematics. Consequently, the study of notions of generalized bounded variation forms an important direction in the field of mathematical analysis. This thesis is devoted to the investiga...
Article
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).
Article
This paper is concerned with the study of two functionals of variational type - the Riesz type generalized variation v_{p,\alpha}(f) (1<p<\infty, 0\le\alpha\le1-1/p) and the moduli of p-continuity \omega_{1-1/p}(f;d). These functionals generate scales of spaces connecting the class of functions of bounded p-variation and the Sobolev space W_p^1. So...
Article
Full-text available
We obtain a necessary and sufficient condition for embeddings of integral Lipschitz classes Lip(\alpha; p) into classes \Lambda BV of functions of bounded \Lambda-variation.
Article
Moduli of p-continuity provide a measure of fractional smoothness of functions via p-variation. We prove a sharp estimate of the modulus of p-continuity in terms of the modulus of q-continuity (1<p<q<∞).
Article
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 investigate various embeddings for mixed norm spaces of bivariate functions whose linear sections have bounded $p$-variation in the sense of Wiener
Article
We obtain estimates of the total p-variation (1<p<∞) and other related functionals for a periodic function f∈L^p[0,1] in terms of its L^p-modulus of continuity ωp(f;δ). These estimates are sharp for any rate of the decay of ω_p(f;δ). Moreover, the constant coefficients in them depend on parameters in an optimal way.

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