Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents linear dynamic component placed between the first two Some common model structures include rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregr...

In this work, we consider the problem of moving average representations for random fields. As in the Kolmogorov–Wiener case, such representations lead to interesting questions in harmonic analysis in the polydisc. In particular, we study outer functions with respect to half-space, semigroup and quarterplane and their interrelations. 2000 Mathematics Subject Classification: 42B30, 60G10, 60G60.

Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator on G. The existence and uniqueness of interpolating variational spline on a graph is shown. As an application of variational splines the paper presents a reconstruction algorithm of PaleyWiener functions o...

Based on a Wiener process approximation, a sequential test for the bundle strength of filaments is proposed and studied here. Asymptotic expressions for the OC and ASN functions are derived, and it is shown that asymptotically the test is more efficient than the usual fixed sample size procedure based on the asymptotic normality of the standardized form of the bundle strength of filaments,

The images of Hermite and Laguerre Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterised. These are used to characterise the image of Schwartz class of rapidly decreasing functions f on Rn and Cn under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for windowed ( short-time) Fourier tran...

This is a survey on reverse Carleson measures for various Hilbert spaces of analytic functions. These spaces include the Hardy, Bergman, certain harmonically weighted Dirichlet, Paley-Wiener, Fock, model (backward shift invariant), and de Branges-Rovnyak spaces. The reverse Carleson measure for backward shift invariant subspaces in the non-Hilbert situation is new.

For the subclasses of nonlinear dynamic systems which can be considered as block oriented systems [8] there exist several identification methods using topologically identical models. One of the simplest nonlinear models of this category is the so-called Wiener model consisting of one linear dynamic block and one nonlinear static block. The Wiener models appear in many engineering applications [...

We define the concepts of stable sampling set, interpolation uniqueness set and complete for a quasinormed space functions apply these to Paley-Wiener spaces Bernstein spaces. obtain sufficient condition on uniformly discrete be an based lemma convergence series in also result transference, Kadec type, property being from with this other which we

A new solution for the problem of selecting poles of the two-parameter Kautz functions in Volterra models is proposed. In general, a large number of parameters are required to represent the Volterra kernels, although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions, such as the Kautz basis. This representation has a Wiener structure consisting of ...