There are perfect construction formulas for the orthonormal uniwavelet. However, it seems that there is not such a good formula with similar structure for multiwavelets. Especially, construction of multiwavelets with dilation factor a(a ≥ 2, a ∈ Z) lacks effective methods. In this paper, a procedure for constructing compactly supported orthonormal multiscale functions is first given, and then b...

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...

Regression or function classes of Euclidean type with compact support and certain smoothness properties are shown to be PAC learnable by the Nadaraya-Watson estimator based on complete orthonormal systems. While requiring more smoothness properties than typical PAC formulations, this estimator is computationally efficient, easy to implement, and known to perform well in a number of practical ap...

Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...

Sets K in d-dimensional Euclidean space are constructed with the property that the inverse Fourier transform of the characteristic function 1 K is a single dyadic orthonormal wavelet. The construction is characterized by its generality in terms of a quantitative iterative procedure, by its computational implementation, and by its simplicity. The general case in which the inverse Fourier transfo...

Vector fitting is widely accepted as a robust macromodelling tool for efficient frequency domain identification of passive components. The orthonormal vector fitting technique is introduced, which improves the numerical stability of the method, by using orthonormal rational functions. This leads to better conditioned equations, reduces the numerical sensitivity to the choice of starting poles s...

We propose a constructive method to find compactly supported orthonormal wavelets for any given compactly supported scaling function φ in the multivariate setting. For simplicity, we start with a standard dilation matrix 2I2×2 in the bivariate setting and show how to construct compactly supported functions ψ1, · · · , ψn with n > 3 such that {2ψj(2x − `, 2ky − m), k, `,m ∈ Z, j = 1, . . . , n} ...

Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a non-linear shrinking of frequencies, the function is transformed into a band-limited one. One may then perform a decomposition in Fourier series. This process gives rise to new orthonormal ...

We study the nonlinear Schr\"odinger equation for systems of $N$ orthonormal functions. prove existence ground states all when exponent $p$ non linearity is not too large, and an infinite sequence $N_j$ tending to infinity in whole range possible $p$'s, dimensions $d\geq1$. This allows us that translational symmetry broken a quantum crystal Kohn-Sham model with large Dirac exchange constant.

We present a scheme that leverage orthonormal or biorthogonal wavelets to a new system of biorthogonal wavelets. The leveraged biorthogonal wavelets will have some nice properties. If we start with orthonormal wavelets, the leveraged scaling functions and wavelets are compactly supported and are diierentiable. The derivatives of the leveraged wavelets are orthogonal to their translations; the d...