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- K-finite abstract "In mathematics, a K-finite function is a type of generalized trigonometric polynomial. Here K is some compact group, and the generalization is from the circle group T. From an abstract point of view, the characterization of trigonometric polynomials amongst other functions F, in the harmonic analysis of the circle, is that for functions F in any of the typical function spaces, F is a trigonometric polynomial if and only if its Fourier coefficients a'nvanish for |n| large enough, and that this in turn is equivalent to the statement that all the translatesF(t + θ)by a fixed angle θ lie in a finite-dimensional subspace. One implication here is trivial, and the other, starting from a finite-dimensional invariant subspace, follows from complete reducibility of representations of T.From this formulation, the general definition can be seen: for a representation ρ of K on a vector space V, a K-finite vector v in V is one for which the ρ(k).vfor k in K span a finite-dimensional subspace. The union of all finite-dimension K-invariant subspaces is itself a subspace, and K-invariant, and consists of all the K-finite vectors. When all v are K-finite, the representation ρ itself is called K-finite.".
- K-finite wikiPageID "11054062".
- K-finite wikiPageLength "1596".
- K-finite wikiPageOutDegree "10".
- K-finite wikiPageRevisionID "627983207".
- K-finite wikiPageWikiLink Category:Representation_theory_of_groups.
- K-finite wikiPageWikiLink Circle_group.
- K-finite wikiPageWikiLink Compact_group.
- K-finite wikiPageWikiLink Complete_reducibility.
- K-finite wikiPageWikiLink Fourier_coefficient.
- K-finite wikiPageWikiLink Fourier_series.
- K-finite wikiPageWikiLink Function_space.
- K-finite wikiPageWikiLink Harmonic_analysis.
- K-finite wikiPageWikiLink Invariant_subspace.
- K-finite wikiPageWikiLink Mathematics.
- K-finite wikiPageWikiLink Semi-simplicity.
- K-finite wikiPageWikiLink Trigonometric_polynomial.
- K-finite wikiPageWikiLinkText "''K''-finite".
- K-finite wikiPageWikiLinkText "K-finite".
- K-finite hasPhotoCollection K-finite.
- K-finite wikiPageUsesTemplate Template:One_source.
- K-finite wikiPageUsesTemplate Template:Ref_improve.
- K-finite subject Category:Representation_theory_of_groups.
- K-finite hypernym Polynomial.
- K-finite type Article.
- K-finite type Article.
- K-finite comment "In mathematics, a K-finite function is a type of generalized trigonometric polynomial. Here K is some compact group, and the generalization is from the circle group T.".
- K-finite label "K-finite".
- K-finite sameAs m.02qzfhc.
- K-finite sameAs Q6322832.
- K-finite sameAs Q6322832.
- K-finite wasDerivedFrom K-finite?oldid=627983207.
- K-finite isPrimaryTopicOf K-finite.