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3,415
Analytical foundations of Volterra series
- Journal of Mathematical Control and Information
, 1984
"... In this paper we carefully study the analysis involved with Volterra series. We address system-theoretic issues ranging from bounds on the gain and incremental gain of Volterra series operators to the existence of Volterra series operator inverses, and mathematical topics such as the relation betwee ..."
Abstract
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Cited by 22 (0 self)
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between Volterra series operators and Taylor series. The proofs are complete, and use only the basic facts of analysis. We prove a general Steady-state theorem for Volterra series operators, and then establish a general formula for the spectrum of the output of a Volterra series operator in terms
Regularization tools – a matlab package for analysis and solution of discrete ill-posed problems
- Numerical Algorithms
, 1994
"... The software described in this report was originally published in Numerical Algorithms 6 (1994), pp. 1–35. The current version is published in Numer. Algo. 46 (2007), pp. 189–194, and it is available from www.netlib.org/numeralgo and www.mathworks.com/matlabcentral/fileexchangeContents ..."
Abstract
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Cited by 276 (8 self)
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The software described in this report was originally published in Numerical Algorithms 6 (1994), pp. 1–35. The current version is published in Numer. Algo. 46 (2007), pp. 189–194, and it is available from www.netlib.org/numeralgo and www.mathworks.com/matlabcentral/fileexchangeContents
Resolvent formula for a Volterra equation in Hilbert space
- SIAM J. Math. Anal
, 1982
"... Let y(t,x,f) denote the solution of the Cauchy problem t y'(t) + f Id + a(t-s)]L y(s)ds = f(t), t> 0, y(O) = x 0 where d> 0 and L is a self-adjoint densely defined linear operator on a Hilbert space H with L> AI I. Let U(t)x = y(t,x,O), V = U'. By analyzing a related scalar equat ..."
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Cited by 1 (0 self)
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Let y(t,x,f) denote the solution of the Cauchy problem t y'(t) + f Id + a(t-s)]L y(s)ds = f(t), t> 0, y(O) = x 0 where d> 0 and L is a self-adjoint densely defined linear operator on a Hilbert space H with L> AI I. Let U(t)x = y(t,x,O), V = U'. By analyzing a related scalar
1Faa ̀ di Bruno’s formula for Gâteaux
"... differentials and interacting stochastic population processes ..."
Jacobi operators and completely integrable nonlinear lattices
- MATHEMATICAL SURVEYS AND MONOGRAPHS
, 2000
"... ..."
What is the relativistic Volterra lattice
- Commun. Math. Phys
, 1999
"... Abstract. We develop a systematic procedure of finding integrable ”relativistic ” (regular one– parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First, for a given system one finds a local discretizatio ..."
Abstract
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Cited by 1 (1 self)
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as to the Volterra lattice and a certain Bogoyavlensky lattice, for which the ”relativistic ” deformations were not known previously.
Nonlinear Black-Box Modeling in System Identification: a Unified Overview
- Automatica
, 1995
"... A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, ..."
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Cited by 213 (15 self)
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, as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what
Results 1 - 10
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