There are several different (sometimes related) mathematical objects called ‘’spectrum’‘ or whose name has ‘’spectral’‘ as prefix:
inlcuding spectral theory such spectrum of an operator, spectra of families, of a Banach algebra, Gelfand spectrum, prime (primitive etc.) spectrum of a commutative ring spectrum of a ring, analytic spectrum, Cole's theory of spectrum, spectrum of an abelian category, Orlov spectrum spectrum of a triangulated category, prime spectrum of a symmetric monoidal stable (∞,1)-category, etc.
There is also a notion of
which has no particular relation to other notions of spectrum, except that filtered spectra give rise to spectral sequences of filtered spectra.
In physics: