10 citations · 17 across the 26 of their papers we have counts for
31 papers
Hyperpositive functions, sector bounded functions and a trace formula
Daniel Alpay, Izchak Lewkowicz
We study an indexed family of functions closely related to functions ana- lytic and with a real positive part in the right open half plane (the so-called positive functions) and to…
Quantitatively hyper-positive real rational functions IV: The canonical case
Daniel Alpay, Izchak Lewkowicz
In the linear time-invariant framework, passive systems are modeled by positive real functions. Dissipative systems can be modeled by the subset of quantita- tively Hyper-positive…
Operator model and a trace formula for pairs of unitary operators
Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz +1
Using the theory of reproducing kernel Hilbert spaces introduced by L. de Branges and J. Rovnyak we prove a trace formula for pairs of operators in Hilbert space in terms of a Cara…
Quantitatively hyper-positive real rational functions III
Daniel Alpay, Izchak Lewkowicz
Hyper-Positive Real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related t…
Representation theory and multilevel filters
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical setting. This is done in a fr…
Discrete Wiener Algebra in the Bicomplex Setting, Spectral Factorization with Symmetry, and Superoscillations
Daniel Alpay, Izchak Lewkowicz, Mihaela Vajiac
In this paper we present parallel theories on constructing Wiener algebras in the bicomplex setting. With the appropriate symmetry condition, the bicomplex matrix valued case can b…