On the relation between positive definite functions and generalized Toeplitz kernels

Author:
J. Friedrich

Journal:
Proc. Amer. Math. Soc. **120** (1994), 727-730

MSC:
Primary 42A82; Secondary 47A57, 47B35

DOI:
https://doi.org/10.1090/S0002-9939-1994-1209422-X

MathSciNet review:
1209422

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Abstract: We show that extension problems for generalized Toeplitz kernels may be completely reduced to extension problems for positive definite functions, where the solution is well known. These considerations in particular imply that generalized Toeplitz kernels may be represented as Fourier transforms of positive operator-valued measures.

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1209422-X

Article copyright:
© Copyright 1994
American Mathematical Society