arXiv subjects

Eduardo Brandani da Silva

Publications and source records attributed to Eduardo Brandani da Silva.

7 recordsLinked to original sources

arXiv2026

A multilinear Zafran theorem for the measure of noncompactness of operators

We establish a multilinear analogue of Zafran's interpolation theorem for operators acting on products of quasi-Banach spaces generated by the general real methods. We consider multilinear operators between quasi-Banach couples and obtain interpolation estimates expressed in terms of the fundamental functions of the underlying sequence spaces. As an application, we study the measure of noncompactness of interpolated multilinear operators in this setting and derive a corresponding interpolation estimate for this quantity. In particular, we obtain a one-sided compactness result for interpolated multilinear operators acting on spaces associated with the abstract real methods. These results recover known bilinear theorems as special cases and extend earlier results on multilinear interpolation and on the interpolation of the measure of noncompactness.

math.FA↗

arXiv2024

New topological subsystem codes from semi-regular tessellations

In this work, we present new constructions for topological subsystem codes using semi-regular Euclidean and hyperbolic tessellations. They give us new families of codes, and we also provide a new family of codes obtained through an already existing construction, due to Sarvepalli and Brown. We also prove new results that allow us to obtain the parameters of these new codes.

cs.IT↗

arXiv2021

Schmidt Representation of Bilinear Operators on Hilbert Spaces

Current work defines Schmidt representation of a bilinear operator $T: H_1 \times H_2 \rightarrow K$, where $H_1, H_2$ and $K$ are separable Hilbert spaces. Introducing the concept of singular value and ordered singular value, we prove that if $T$ is compact, and its singular values are ordered, then $T$ has a Schmidt representation on real Hilbert spaces. We prove that the hypothesis of existence of ordered singular values is fundamental.

math.FA↗

arXiv2018

Hyperbolic quantum color codes

Current work presents a new approach to quantum color codes on compact surfaces with genus $g \geq 2$ using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations. We show that this method may give rise to color codes with a very good parameters and we present tables with several examples of these codes whose parameters had not been shown before. We also present a family of codes with minimum distance $d=4$ and the encoding rate asymptotically going to 1 while $n \rightarrow \infty$.

quant-ph↗

arXiv2017

New Young inequalities and applications

We establish upper bounds for the convolution operator acting between interpolation spaces. This will provide several examples of Young Inequalities in different families of function spaces. We use this result to prove a bilinear interpolation theorem and we show applications to the study of bilinear multipliers.

math.FA↗

arXiv2014

Space-Time Codes from Spectral Norm: A Fresh Look

Current research proposes a natural environment for the space-time codes and in this context it is obtained a new design criterion for space-time codes in multi-antenna communication channels. The objective of this criterion is to minimize the pairwise error probability of the maximum likelihood decoder, endowed with the matrix spectrum norm. The random matrix theory is used and an approximation function for the probability density function is obtained for the largest eigenvalue of a Wishart Matrix.

cs.IT↗

arXiv2012

Interpolation of bilinear operators and compactness

The behavior of bilinear operators acting on interpolation of Banach spaces for the $ρ$ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Person's compactness theorems are obtained for the bilinear case and the $ρ$ method.

math.FA↗