Abstract. Let $F$ be a measurable $\kappa $-indefinite generalized Toeplitz kernel defined on a, finite or infinite, interval. We prove that $F = F^{(c)} + F^{(o)}$, where $F^{(c)}$ is a $\kappa $-indefinite generalized Toeplitz kernel given by four continuous functions and $F^{(o)}$ is a positive definite generalized Toeplitz kernel which vanishes almost everywhere. We also prove an extension result for measurable $\kappa $-indefinite generalized Toeplitz kernels defined on a finite interval.
AMS Subject Classification
(1991): 47B50, 47D03, 46C20, 28A20
Keyword(s):
indefinite kernel,
indefinite metric space,
measurable,
reproducing kernel space,
semigroups of operators,
Toeplitz kernel
Received February 4, 2011, and in revised form March 10, 2011. (Registered under 9/2011.)
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