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Norms of sampling operators

✍ Scribed by P. Zizler

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 264 KB
Volume: 277
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)10066-0

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✦ Synopsis

Let h(z) be an essentially bounded complex valued function on the unit circle Y = {z I Iz] = 1}. Consider the corresponding Laurent operator Lt, = (h= m),.meZ, where h= is the nth Fourier coefficient of h(z), h,, = fT h(z)z " dz. Let us consider an operator Sh(p,q), which we shall call a sampling operator, defined as Sh(p,q)= (hpn-qm)n,m6Z, where p, q E N = {1,2,.. ,}. These operators are obtained from Lh by "keeping" every qth column and everypth row in the bi-infinite matrix Lb. In our paper, we find an upper and lower bound for the norm of the operator Sh(p,q).

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