An orthonormal basis adaptation method for function approximation was developed and applied to reinforcement learning with multi-dimensional continuous state space. First, a basis used for linear function approximation of a control function is set to an orthonormal basis. Next, basis elements with small activities are replaced with other candidate elements as learning progresses. As this replac...

Let X be an R-fold, and let π : E −→ X be a real vector bundle, of rank r, equipped with a positive definite symmetric bilinear form. If e1, . . . , er ∈ π −1(X) are orthonormal, then e1 ∧ · · · ∧ er is a non-trivial vector in ∧r E. Proposition: If f1, . . . , fr is any other orthonormal basis for π −1(X), then e1 ∧ · · · ∧ er = ±f1 ∧ · · · ∧ fr. Proof. Note that fi = g · ei for g ∈ O(r), so de...

Weaving frames have potential applications in wireless sensor networks that require distributed processing of signals under different frames. In this paper, we study some new properties weaving generalized (or g-frames) and orthonormal bases g-orthonormal bases). It is shown a g-frame its dual are woven. The inter-relation optimal bounds universal studied. Further, present characterization g-fr...

Given a C-function f on a compact riemannian manifold (X, g) we give a set of frequencies L = Lf (ε) depending on a small parameter ε > 0 such that the relative L-error ‖f−f ‖ ‖f‖ is bounded above by ε, where f L denotes the L-partial sum of the Fourier series f with respect to an orthonormal basis of L(X) constituted by eigenfunctions of the Laplacian operator ∆ associated to the metric g.

The objective of this paper is to construct wavelet packets associated with multiresolution analysis on locally compact Abelian groups. Moreover, from the collection of dilations and translations of the wavelet packets, we characterize the subcollections which form an orthonormal basis for L(G).

Abstract. In this paper, we mainly parameterize g-frames in Hilbert space in terms of operators. Firstly, under the condition that there exists a g-orthonormal basis we establish the one to one correspondence between different kinds of g-frames with certain kinds of operators. Then we parameterize g-frames without the above restriction. Finally, we consider some special g-frames, and their oper...

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...