hilbert spaces

The geometry of Hilbert spaces: infinite-dimensional geometry

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The geometry of Hilbert spaces represents a revolution in the way we understand mathematics and physics. It opens the door to a deeper understanding of infinite structures and allows us to explore phenomena that are sometimes counter-intuitive related to infinite dimensions. The complexity of this infinite-dimensional geometry is revealed through fundamental concepts such as the … Read more

Functional analysis: Banach and Hilbert spaces

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Functional analysis is a fundamental pillar of modern mathematics, primarily revolving around the concepts of normed vector spaces and linear operators. Among these spaces, Banach and Hilbert spaces hold a central position due to their structural richness and multiple applications, particularly in the resolution of differential equations, optimization, and applied sciences. Understanding the nature of … Read more