3 citations · 5 across the 10 of their papers we have counts for
14 papers
A new convergence proof for an iterative scheme for elliptic Cauchy problems based on alternating orthogonal projections
Abhijit Guchhait, Adrian Muntean, Martin Lind
We consider an elliptic Cauchy problem for the Poisson equation in which both Dirichlet and Neumann boundary data are prescribed only on a portion of the boundary, while no boundar…
On the -variation of Riemann's "nondifferentiable'' function
Martin Lind
We investigate the variational properties of Riemann's ''nondifferentiable'' function . We show that has finite -variation for and infinite -variation for $p<4…
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 -variation , a family of functionals that interpolates between Wiener -variation and t…
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 and arbitrary , we construct a Lipschitz perturbation w…
Fourier transform inequalities, lattice point discrepancy, asymptotic behavior, oscillatory integrals
Martin Lind
For , we establish sharp inequalities for the Fourier transform of the characteristic function of the -unit ball . We show that $$ \sup_{\bol…
A sharp estimate of the discrepancy of a certain numerical sequence
Martin Lind
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 s…
The modulus of -variation and its applications
Gholam Hossein Esslamzadeh, Milad Moazami Goodarzi, Mahdi Hormozi +1
In this note, we introduce the notion of modulus of -variation for a function of a real variable, and show that it serves in at least two important problems, namely, the uniform…
An extension of Koksma's inequality
Martin Lind
When applying the quasi-Monte Carlo (QMC) method of numerical integration of univariate functions, Koksma's inequality provides a basic estimate of the error in terms of the discre…
A semidiscrete Galerkin scheme for a coupled two-scale elliptic-parabolic system: well-posedness and convergence approximation rates
Martin Lind, Adrian Muntean, Omar Richardson
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 inte…
Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system
Martin Lind, Adrian Muntean, Omar Richardson
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…
A priori feedback estimates for multiscale reaction-diffusion systems
Martin Lind, Adrian Muntean
We study the approximation of a multiscale reaction-diffusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done via micro-macro…
Nonlinear nonnested 2-D spline approximation
Martin Lind, Pencho Petrushev
Nonlinear approximation from regular piecewise polynomials (splines) of degree supported on rings in is studied. By definition a ring is a set in obtained by sub…
On functions of bounded -variation and integral smoothness
Martin Lind
We obtain a necessary and sufficient condition for embeddings of integral Lipschitz classes Lip(α; p) into classes ΛBV of functions of bounded Λ-variation.
On embeddings of spaces of bivariate functions of bounded -variation
Martin Lind
We obtain sharp estimates of the Hardy-Vitali type total -variation of a function of two variables in terms of its mixed modulus of continuity in . We also investi…