arXiv subjects

M. T. Malheiro

Publications and source records attributed to M. T. Malheiro.

3 recordsLinked to original sources

arXiv2026

The structural method for Ordinary Differential Equations

We design and analyse a new numerical method to solve ODE system based on the structural method. We compute approximations of solutions together with its derivatives up to order $K$ by solving an entire block corresponding to $R$ time steps. We build the physical relations that connect the function and derivative approximations at each time step by using the ODE and its derivatives, and develop the structural equations that establish linear relations between the function and its derivative over the whole block of $R$ times steps. The non-linear system is solved and provide very accurate approximations with nice spectral resolution properties.

math.NA↗

arXiv2015

Model spaces and Toeplitz kernels in reflexive Hardy spaces

This paper considers model spaces in an $H_p$ setting. The existence of unbounded functions and the characterisation of maximal functions in a model space are studied, and decomposition results for Toeplitz kernels, in terms of model spaces, are established.

math.FA↗

arXiv2011

Factorization in a torus and Riemann-Hilbert problems

A new concept of meromorphic $Σ$-factorization, for Hölder continuous functions defined on a contour $Γ$ that is the pullback of $\dot{\mathbb{R}}$ (or the unit circle) in a Riemann surface $Σ$ of genus 1, is introduced and studied, and its relations with holomorphic $Σ$-factorization are discussed. It is applied to study and solve some scalar Riemann-Hilbert problems in $Σ$ and vectorial Riemann-Hilbert problems in $\mathbb{C}$, including Wiener-Hopf matrix factorization, as well as to study some properties of a class of Toeplitz operators with $2 \times 2$ matrix symbols.

math.CV↗