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The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum
Daniel Alpay, Fabrizio Colombo, David P. Kimsey
In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of -spectrum. The proof technique consists of first establishing a spect…
Boundary interpolation for slice hyperholomorphic Schur functions
K. Abu-Ghanem, D. Alpay, F. Colombo +2
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers , quaternions …
The spectral theorem for unitary operators based on the -spectrum
D. Alpay, F. Colombo, D. P. Kimsey +1
The quaternionic spectral theorem has already been considered in the literature, see e.g. [22], [31], [32], however, except for the finite dimensional case in which the notion of s…
An extension of Herglotz's theorem to the quaternions
D. Alpay, F. Colombo, D. P. Kimsey +1
A classical theorem of Herglotz states that a function from into is positive definite if and only there exists a $\mathbb C^{s\t…