ACTA issues

Representation of generalized Toeplitz kernels with a finite number of negative squares

Ramón Bruzual, Marisela Domínguez, Boris Lora

Acta Sci. Math. (Szeged) 78:1-2(2012), 111-128

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.)