Many nonlinear systems can be described by a Wiener-Schetzen model. In this model, the linear dynamics are formulated in terms of orthonormal basis functions (OBFs). The nonlinearity is modeled by a multivariate polynomial. In general, an infinite number of OBFs is needed for an exact representation of the system. This paper considers the approximation of a Wiener system with finite-order infin...

In this paper, model sets for continuous–time linear time invariant systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalise the well known Laguerre and two–parameter Kautz cases. It is shown that the obtained model sets are norm dense in the Hardy space H1(Π) under the same condition as previously derived by the authors for the norm denseness in the (Π ...

Abstract We prove that a finite index regular inclusion of $II_1$ -factors with commutative first relative commutant is always crossed product subfactor respect to minimal action biconnected weak Kac algebra. Prior this, we every which depth 2 and has simple (respectively, or commutant) admits two-sided Pimsner–Popa basis unitary orthonormal basis).

Orthonormal spin-flavor wave functions of Lorentz covariant quark models of the Bakamjian-Thomas type are constructed for nucleon resonances. Three different bases are presented. The manifestly Lorentz covariant Dirac-Melosh basis is related to the Pauli-Melosh basis and the symmetrized Bargmann-Wigner basis that are manifestly orthogonal.

We analyze all orthonormal bases of exponentials on the Cantor set defined by Jorgensen and Pedersen in J. Anal. Math. 75,1998, pp 185-228. A complete characterization for all maximal sets of orthogonal exponentials is obtained by establishing a one-to-one correspondence with the spectral labelings of the infinite binary tree. With the help of this characterization we obtain a sufficient condit...

fusion is a developmental anomaly defined as the :union: of two normally separated tooth buds or the partial splitting of one tooth bud into two buds. depending on the stage of development, fusion may be either complete or incomplete. the significance of this particular case was that this fusion occurred in a posterior permanent mandibular tooth, while such a manifestation is more reported in m...

We construct a new orthonormal basis for L(R), whose elements are angularly integrated ridge functions — orthonormal ridgelets. The new basis functions are in L(R) and so are to be distinguished from the ridge function approximation system called ridgelets by Candès (1997, 1998), as ridge functions are not in L(R). Orthonormal ridgelet expansions have an interesting application in nonlinear app...

In this paper we develop a sublinear-time compressive sensing algorithm for approximating functions of many variables which are compressible in given Bounded Orthonormal Product Basis (BOPB). The resulting is shown to both have an associated best s-term recovery guarantee the BOPB, and also work well numerically solving sparse approximation problems involving contained span fairly general sets ...

Our proof of [1, Theorem 1.1] is partially incorrect. The reason that, contrary to what we claimed, the construction space $${\mathscr {H}}^s$$ depends on orthonormal basis $$(\rho _k)$$ . We give in present note a new that needs little bit stronger assumption.