We investigate properties of subspaces of L2 spanned by subsets of a finite orthonormal system bounded in the L∞ norm. We first prove that there exists an arbitrarily large subset of this orthonormal system on which the L1 and the L2 norms are close, up to a logarithmic factor. Considering for example the Walsh system, we deduce the existence of two orthogonal subspaces of L2 , complementary to...

Today, companies need to make use of appropriate patterns such as supply chain management system to gain and preserve a position in competitive world-wide market. Supply chain is a large scaled network consists of suppliers, manufacturers, warehouses, retailers and final customers which are in coordination with each other in order to transform products from raw materials into finished goods wit...

A least-squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions. The basis functions are orthogonal in 8$, and generalize the pulse, Laguerre and Kautz bases. One of their important properties is that, when chosen properly, ...

Any non-complete orthonormal system in a Hilbert space can be transformed into basis by small perturbations.

A new class of canonical forms is given proposed in which (A,C) is in Hessenberg observer or Schur form and output normal: I − A∗A = C∗C. Here, C is the d × n measurement matrix and A is the advance matrix. The (C,A) stack is expressed as the product of n orthogonal matrices, each of which depends on d parameters. State updates require onlyO(nd) operations and derivatives of the system with res...

Abstract There has re ently been interest in the use of orthonormal bases for the purposes of SISO system identi ation. Con urrently, but separately, there has also been vigorous work on estimation of MIMO systems by omputationally heap and reliable s hemes. These latter ideas have olle tively be ome known as `4SID' methods. This paper is a ontribution overlapping these two s hools of thought b...

It is very important for generating an orthonormal multiwavelet system to construct a conjugate quadrature filter (CQF). In this paper, a general method of constructing a length-J + 1 CQF with multiplicity r and scale a from a length-J CQF is obtained. As a special case, we study generally the construction of a length-J + 1 CQF with multiplicity 2 and scale 2 which can generate a compactly supp...

Let {4>„{dfi)} be a system of orthonormal polynomials on the unit circle with respect to d/i and {y/„,m(dß)} be a system of orthonormal polynomials on the unit circle with respect to the varying measures dß/\wn(z)\2, z = e'e , where {w„(z)} is a sequence of polynomials, degw« = n , whose zeros w„ i, ... , wn,n lie in \z\ < 1 The asymptotic behavior of the ratio of the two systems on and outside...

Consider the sequence of poles A = {α1, α2, . . .}, and suppose the rational functions φn with poles inA form an orthonormal system with respect to an Hermitian positive-definite inner product. Further, assume the φn satisfy a three-term recurrence relation. Let the rational function φ n\1 with poles in {α2, α3, . . .} represent the associated rational function of φn of order 1; i.e. the φ n\1 ...