5 citations · 9 across the 6 of their papers we have counts for
5 papers
The spectral theorem for normal operators on a Clifford module
Fabrizio Colombo, David P. Kimsey
In this paper, using the recently discovered notion of the -spectrum, we prove the spectral theorem for a bounded or unbounded normal operator on a Clifford module (i.e., a two-…
Wiener algebra for the quaternions
Daniel Alpay, Fabrizio Colombo, David P. Kimsey +1
We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-Lévy type theorem and a factoriz…
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…