10 citations · 10 across the 5 of their papers we have counts for
5 papers · 1 filter
On Pseudo-Spectral Factorization over the Complex Numbers and Quaternions
Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz +1
This paper is a continuation of the research of our previous work and considers quaternionic generalized Carathéodory functions and the related family of generalized positive funct…
Positive and generalized positive real lemma for slice hyperholomorphic functions
D. Alpay, F. Colombo, I. Lewkowicz +1
In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic function…
Composition of rational functions: state-space realization and applications
Daniel Alpay, Izchak Lewkowicz
We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding sta…
Interpolation by polynomials with symmetries on the imaginary axis
Daniel Alpay, Izchak Lewkowicz
We here specialize the standard matrix-valued polynomial interpolation to the case where on the imaginary axis the interpolating polynomials admit various symmetries: Positive semi…
Extending wavelet filters. Infinite dimensions, the non-rational case, and indefinite-inner product spaces
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
In this paper we are discussing various aspects of wavelet filters. While there are earlier studies of these filters as matrix valued functions in wavelets, in signal processing, a…