10 citations · 109 across the 105 of their papers we have counts for
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Characterizations of families of rectangular finite impulse response, para-unitary systems
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
We here study Finite Impulse Response (FIR) rectangular, not necessarily causal, systems which are (para)-unitary on the unit circle (=the class ). First, we offer thr…
Wiener-Chaos Approach to Optimal Prediction
Daniel Alpay, Alon Kipnis
The chaos expansion of a general non-linear function of a Gaussian stationary increment process conditioned on its past realizations is derived. This work combines Wiener chaos exp…
Characterizations of rectangular (para)-unitary rational Functions
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
We here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle: (i) Through the realization matrix of Schur stabl…
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…
A new realization of rational functions, with applications to linear combination interpolation
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz +1
We introduce the following linear combination interpolation problem (LCI): Given distinct numbers and complex numbers and , find all…
Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization
Daniel Alpay, Fabrizio Colombo, Irene Sabadini
In this paper we prove a new version of Krein-Langer factorization theorem in the slice hyperholomorphic setting which is more general than the one proved in [D. Alpay, F. Colombo,…