algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
In the spectral theory of operator algebras, the discrete spectrum is that part of the spectrum of a linear operator which looks like the set of eigenvalues of a matrix, hence of a linear operator acting on a finite-dimensional vector space/finite-dimensional Hilbert space.
The discrete spectrum of a closed linear operator on a Hilbert space consists of those points in its operator spectrum which are
isolated points: they have an open neighbourhood containing no other points of the spectrum,
of finite algebraic multiplicity.
The second clause simplifies for self-adjoint operators, where it is equivalent to corresponding eigenspace being finite-dimensional (cf. Moretti 2017 Rem. 9.15), hence to the condition that the geometric multiplicity is finite.
The discrete spectrum is a subset of the point spectrum, but does in general not coincide with the point spectrum.
See most of the references listed at operator spectrum and spectral theory, for instance
See also
Last revised on November 13, 2025 at 10:55:42. See the history of this page for a list of all contributions to it.