Hilbert space

Hilbert space, in mathematics, an example of an infinite-dimensional space that had a major impact in analysis and topology. The German mathematician David Hilbert first described this space in his work on integral equations and Fourier series, which occupied his attention during the period 1902–12. The points of Hilbert space are infinite sequences (x₁, x₂, x₃, …) of real numbers that are square summable, that is, for which the infinite series x₁² +  x₂² +  x₃² + … converges...