Rigged Hilbert space
HILBERT SPACE EQUIPPED WITH A DENSE SUBSPACE THAT CARRIES (IN ADDITION TO THE SUBSPACE TOPOLOGY) A FINER TOPOLOGY SUCH THAT THE INCLUSION MAP IS CONTINUOUS
Generalized eigenspaces of unbounded continuous operators; Generalized eigenspaces of unbounded operators; Generalized eigenfunction; Generalised eigenfunction; Gelfand triple; Nested Hilbert space; Equipped Hilbert space; Rigged hilbert space; Banach Gelfand triple; (Banach) Gelfand triple
In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis. Such spaces were introduced to study spectral theory in the broad sense.