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Full-Text Articles in Algebra
On The Characteristics Of A Class Of Gaussian Processes Within The White Noise Space Setting, Daniel Alpay, Haim Attia, David Levanony
On The Characteristics Of A Class Of Gaussian Processes Within The White Noise Space Setting, Daniel Alpay, Haim Attia, David Levanony
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using the white noise space framework, we define a class of stochastic processes which include as a particular case the fractional Brownian motion and its derivative. The covariance functions of these processes are of a special form, studied by Schoenberg, von Neumann and Krein.
Linear Stochastic State Space Theory In The White Noise Space Setting, Daniel Alpay, David Levanony, Ariel Pinhas
Linear Stochastic State Space Theory In The White Noise Space Setting, Daniel Alpay, David Levanony, Ariel Pinhas
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring, and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant, stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system, namely its average behavior.
Regular Functions On The Space Of Cayley Numbers, Graziano Gentili, Daniele C. Struppa
Regular Functions On The Space Of Cayley Numbers, Graziano Gentili, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we present a new definition of regularity on the space Ç of Cayley numbers (often referred to as octonions), based on a Gateaux-like notion of derivative. We study the main properties of regular functions, and we develop the basic elements of a function theory on Ç. Particular attention is given to the structure of the zero sets of such functions.
Krein Systems And Canonical Systems On A Finite Interval: Accelerants With A Jump Discontinuity At The Origin And Continuous Potentials, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich
Krein Systems And Canonical Systems On A Finite Interval: Accelerants With A Jump Discontinuity At The Origin And Continuous Potentials, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich
Mathematics, Physics, and Computer Science Faculty Articles and Research
This paper is devoted to connections between accelerants and potentials of Krein systems and of canonical systems of Dirac type, both on a finite interval. It is shown that a continuous potential is always generated by an accelerant, provided the latter is continuous with a possible jump discontinuity at the origin. Moreover, the generating accelerant is uniquely determined by the potential. The results are illustrated on pseudo-exponential potentials. The paper is a continuation of the earlier paper of the authors [1] dealing with the direct problem for Krein systems.
Linear Stochastic Systems: A White Noise Approach, Daniel Alpay, David Levanony
Linear Stochastic Systems: A White Noise Approach, Daniel Alpay, David Levanony
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using the white noise setting, in particular the Wick product, the Hermite transform, and the Kondratiev space, we present a new approach to study linear stochastic systems, where randomness is also included in the transfer function. We prove BIBO type stability theorems for these systems, both in the discrete and continuous time cases. We also consider the case of dissipative systems for both discrete and continuous time systems. We further study ℓ1-ℓ2 stability in the discrete time case, and L2-L∞ stability in the continuous time case.
Discrete-Time Multi-Scale Systems, Daniel Alpay, Mamadou Mboup
Discrete-Time Multi-Scale Systems, Daniel Alpay, Mamadou Mboup
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the poly-disc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.