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Encyclopedia > Biorthogonal system

In mathematics, a biorthogonal system in a pair of topological vector spaces E and F that are in duality is a pair of indexed subsets

vi in E

and

wi in F

such that

<vi,wj> = δij

with the Kronecker delta. This applies, for example, with E = F = H a Hilbert space; in which case this reduces to an orthonormal system. In L2[0,2π] the functions cos nx and sin nx form a biorthogonal system.


Reference

  • Jean Dieudonné, On biorthogonal systems Michigan Math. J. 2 (1953), no. 1, 7–20 [1] (http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.mmj/1028989861)



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