Abstract
A special case of our extension question for continuous positive definite (p.d.) functions on a fixed finite interval \(\left \vert x\right \vert < a\) in \(\mathbb{R}\) is the following: It offers a spectral model representation for ALL Hermitian operators with dense domain in Hilbert space and with deficiency indices \(\left (1,1\right )\). (See e.g., [vN32a, Kre46, DS88, AG93, Nel69].)
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References
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Jorgensen, P., Pedersen, S., Tian, F. (2016). Models for, and Spectral Representations of, Operator Extensions. In: Extensions of Positive Definite Functions. Lecture Notes in Mathematics, vol 2160. Springer, Cham. https://doi.org/10.1007/978-3-319-39780-1_10
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DOI: https://doi.org/10.1007/978-3-319-39780-1_10
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