Spectral representation for generalized operator-valued Toeplitz kernels

We prove an integral representation for operator-valued Toeplitz kernels. The proof is based on the spectral theory of the corresponding differential operator constructed from this kernel and acting in a Hilbert space. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1698–1710, December, 2005.