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  2. Spectrum (functional analysis) - Wikipedia

    en.wikipedia.org/wiki/Spectrum_(functional_analysis)

    In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix.

  3. Discrete spectrum (mathematics) - Wikipedia

    en.wikipedia.org/.../Discrete_spectrum_(Mathematics)

    A point in the spectrum of a closed linear operator: in the Banach space with domain is said to belong to discrete spectrum of if the following two conditions are satisfied: [1] λ {\displaystyle \lambda } is an isolated point in σ ( A ) {\displaystyle \sigma (A)} ;

  4. Spectral theory - Wikipedia

    en.wikipedia.org/wiki/Spectral_theory

    The spectrum of T is the set of all complex numbers ζ such that R ζ fails to exist or is unbounded. Often the spectrum of T is denoted by σ(T). The function R ζ for all ζ in ρ(T) (that is, wherever R ζ exists as a bounded operator) is called the resolvent of T. The spectrum of T is therefore the complement of the resolvent set of T in ...

  5. Spectrum (topology) - Wikipedia

    en.wikipedia.org/wiki/Spectrum_(topology)

    2.6 Ω-spectrum. 2.7 Ring spectrum. 3 ... Download as PDF; Printable version ... In algebraic topology, a branch of mathematics, a spectrum is an object representing ...

  6. Essential spectrum - Wikipedia

    en.wikipedia.org/wiki/Essential_spectrum

    In mathematics, the essential spectrum of a bounded operator (or, more generally, of a densely defined closed linear operator) is a certain subset of its spectrum, defined by a condition of the type that says, roughly speaking, "fails badly to be invertible".

  7. Spectral graph theory - Wikipedia

    en.wikipedia.org/wiki/Spectral_graph_theory

    A pair of graphs are said to be cospectral mates if they have the same spectrum, but are non-isomorphic. The smallest pair of cospectral mates is {K 1,4, C 4 ∪ K 1}, comprising the 5-vertex star and the graph union of the 4-vertex cycle and the single-vertex graph [1].

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