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Slant Hankel operators

Subhash Chander AroraRuchika BatraM. P. Singh — 2006

Archivum Mathematicum

In this paper the notion of slant Hankel operator K ϕ , with symbol ϕ in L , on the space L 2 ( 𝕋 ) , 𝕋 being the unit circle, is introduced. The matrix of the slant Hankel operator with respect to the usual basis { z i : i } of the space L 2 is given by α i j = a - 2 i - j , where i = - a i z i is the Fourier expansion of ϕ . Some algebraic properties such as the norm, compactness of the operator K ϕ are discussed. Along with the algebraic properties some spectral properties of such operators are discussed. Precisely, it is proved that for an invertible...

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