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The spectral form of the functional model for maximally dissipative operators: A Lagrange identity approach
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by M. Brown, M. Marletta, S. N. Naboko and I. Wood

St. Petersburg Math. J. 35 (2024), 25-59

DOI: https://doi.org/10.1090/spmj/1792

Published electronically: April 12, 2024

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Abstract:

This paper is a contribution to the theory of functional models. In particular, it develops the so-called spectral form of the functional model where the selfadjoint dilation of the operator is represented as the operator of multiplication by an independent variable in some auxiliary vector-valued function space. With the help of a Lagrange identity, in the present version the relationship between this auxiliary space and the original Hilbert space will be explicit. A simple example is provided.

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