Search Results - "Alpay, Daniel"

Finitely additive functions in measure theory and applications by Alpay, Daniel, Jorgensen, Palle

“…In this paper, we consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not…”
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Operators induced by certain hypercomplex systems by Alpay, Daniel, Cho, Ilwoo

“…In this paper, we consider a family \(\{ \mathbb{H}_{t}\}_{t\in\mathbb{R}}\) of rings of hypercomplex numbers, indexed by the real numbers, which contain both…”
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Adaptive orthonormal systems for matrix-valued functions by ALPAY, DANIEL, COLOMBO, FABRIZIO, QIAN, TAO, SABADINI, IRENE

“…In this paper we consider functions in the Hardy space \mathbf {H}_2^{p\times q} defined in the unit disc of matrix-valued functions. We show that it is…”
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New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry by Alpay, Daniel, Jorgensen, Palle E.T.

“…We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a…”
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Relative reproducing kernel Hilbert spaces by ALPAY, DANIEL, JORGENSEN, PALLE, VOLOK, DAN

“…We introduce a reproducing kernel structure for Hilbert spaces of functions where differences of point evaluations are bounded. The associated reproducing…”
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Stochastic Wiener filter in the white noise space by Alpay, Daniel, Pinhas, Ariel

“…In this paper we introduce a new approach to the study of filtering theory by allowing the system's parameters to have a random character. We use Hida's white…”
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Positive definite functions and dual pairs of locally convex spaces by Alpay, Daniel, Gabriyelyan, Saak

“…Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we…”
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Characterizations of rectangular (para)-unitary rational functions by Alpay, Daniel, Jorgensen, Palle, Lewkowicz, Izchak

“…We here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle: (i) through the realization…”
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A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes by Alpay, Daniel, Kipnis, Alon

“…Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô…”
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Quantitatively hyper-positive real rational functions II by Alpay, Daniel, Lewkowicz, Izchak

“…Colloquially, quantitatively Hyper-Positive functions form a sub-family of the “Strictly Positive real” functions, where in addition state-space realization…”
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Schur analysis over the unit spectral ball by Alpay, Daniel, Cho, Ilwoo

“…We begin a study of Schur analysis when the variable is now a matrix rather than a complex number. We define the corresponding Hardy space, Schur multipliers…”
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Schur analysis and discrete analytic functions: Rational functions and co-isometric realizations by Alpay, Daniel, Volok, Dan

“…We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers…”
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White noise based stochastic calculus associated with a class of Gaussian processes by Alpay, Daniel, Attia, Haim, Levanony, David

“…Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus…”
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Cauchy-Weil formula, Schur-Agler type classes, new Hardy spaces of the polydisk and interpolation problems by Alpay, Daniel, Yger, Alain

“…Given n rational inner functions Φ=(Φ1,...,Φn) defining a 0-dimensional (hence finite) complete intersection in the polydisk Dn and a Weil polyhedron ΔrΦ…”
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On realization of left and right products of rational functions by Alpay, Daniel, Lewkowicz, Izchak

“…Let F(z) and G(z) be matrix-valued rational functions so that both product functions (FG)(z) and (GF)(z) are well defined. We here explore inter-relations…”
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Quantitatively hyper-positive real functions by Alpay, Daniel, Lewkowicz, Izchak

“…Hyper-positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive…”
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Reflection positivity via Krein space analysis by Alpay, Daniel, Jorgensen, Palle

“…We study reflection positivity in the context of Hilbert space, and Krein-space theory. Our context is that of triple systems (U,J,M+) assumed to satisfy the…”
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A note on the complex and bicomplex valued neural networks by Alpay, Daniel, Diki, Kamal, Vajiac, Mihaela

“…In this paper we first write a proof of the perceptron convergence algorithm for the complex multivalued neural networks (CMVNNs). Our primary goal is to…”
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Interpolation with symmetry and a Herglotz theorem in the bicomplex setting by Alpay, Daniel, Lewkowicz, Izchak, Vajiac, Mihaela

“…We present a new approach to Schur analysis in the bicomplex setting, reducing the various underlying questions to interpolation problems in the complex…”
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Beurling–Lax type theorems in the complex and quaternionic setting by Alpay, Daniel, Sabadini, Irene

“…We give a generalization of the Beurling–Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the…”
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