Rigged Hilbert space
In mathematics and physics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction which can enlarge a Hilbert space to a bigger space containing additional objects which are not in the Hilbert space but which one would like to think of alongside the Hilbert space. For example, in the quantum mechanical description of a non-relativistic particle using the Hilbert space of square-integrable functions on the real line, eigenstates of the position and momentum operators are not in the Hilbert space, but are in a suitably defined rigged Hilbert space.