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Spectral geometry is a field in mathematics which concerns relationships between geometric structures of manifolds and spectra of canonically defined differential operators. ...
The free spectral range of a diffraction grating is the largest wavelength range for a given order that does not overlap the same range in an adjacent order. If the ( m + 1)-th order of λ {\displaystyle \lambda } and m -th order of ( λ + Δ λ ) {\displaystyle (\lambda +\Delta \lambda )} lie at the same angle, then
In stable homotopy theory, a branch of mathematics, the sphere spectrum S is the monoidal unit in the category of spectra. It is the suspension spectrum of S 0 , i.e., a set of two points. Explicitly, the n th space in the sphere spectrum is the n -dimensional sphere S n , and the structure maps from the suspension of S n to S n +1 are the ...
The set of approximate eigenvalues (which includes the point spectrum) is called the approximate point spectrum of T, denoted by σ ap (T). λ ∈ σ ( T ) {\displaystyle \lambda \in \sigma (T)} if T − λ I {\displaystyle T-\lambda I} does not have dense range.
In commutative algebra, the prime spectrum (or simply the spectrum) of a commutative ring is the set of all prime ideals of , and is usually denoted by ; [1] in algebraic geometry it is simultaneously a topological space equipped with the sheaf of rings.
In mathematics, the spectrum of a C*-algebra or dual of a C*-algebra A, denoted Â, is the set of unitary equivalence classes of irreducible *-representations of A.A *-representation π of A on a Hilbert space H is irreducible if, and only if, there is no closed subspace K different from H and {0} which is invariant under all operators π(x) with x ∈ A.
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