This paper deals with continuous frames and continuous Riesz bases. We introduce continuous Riesz bases and give some equivalent conditions for a continuous frame to be a continuous Riesz basis. It is certainly possible for a continuous frame to have only one dual. Such a continuous frame is called a Riesz-type frame [13]. We show that a continuous frame is Riesz-type if and only if it is a con...

LetM be an n-dimensional Riemannian manifold. ThenM is a differentiable manifold with a smoothly varying inner product 〈, 〉x on each tangent space TxM . An orthonormal frame at the point x ∈ M is an orthonormal basis {e1, . . . , en} of the tangent space TxM . The set of orthonormal frames at each point is isomorphic to the Lie group O(n), and the set of orthonormal frames on M forms a principa...

Abstract. A Weyl-Heisenberg frame for L(R) is a frame consisting of translates and modulates of a fixed function in L(R), i.e. (EmbTnag)m,n∈Z , with a, b > 0, and g ∈ L(R). In this paper we will give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g so that (EmbTnag) is an orthonormal basis for L (R). These resu...

This paper proposes a new subspace identification algorithm for continuous-time systems using generalized orthonormal basis functions. It is shown that a generalized orthonormal basis induces the transformation of continuoustime stochastic systems into discrete-time stochastic systems, and that the transformed noises have the ergodicity properties. With these basic observations, the standard su...

It is a well known fact that any orthonormal basis in L 2 can produce a \random density". If fng is an orthonormal basis and fang is a sequence of random variables such that a 2 n = 1 a.s., then f(x) = jann(x)j 2 is a random density. In this note we deene a random density via orthogonal bases of wavelets and explore some of its basic properties.

Orthonormal ridgelets are a specialized set of angularly-integrated ridge functions which make up an orthonormal basis for L2(R). In this paper we explore the relationship between orthonormal ridgelets and true ridge functions r(x1 cos θ + x2 sin θ). We derive a formula giving the ridgelet coefficients of a ridge function in terms of the 1-D wavelet coefficients of the ridge profile r(t), and w...

In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and Schaefer in [6] and used recently in some applications (see [3]). In the case of an orthonormal basis our estimate reduces to Kadec’ optimal 1/4 re...

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalized orthonormal basis functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and ...

In this paper we propose a new modeling technique for LTI multivariable systems using the generalized Orthonormal basis functions with ordinary poles. Once the model structure is built we proceed to update the membership set of the resulting model parameters through the execution of unknown but bounded error identification algorithms. This updating aims to synthesize a robust control strategy. ...