The recent emergence of the discrete fractional Fourier transform has spurred research activity aiming at generating Hermite-Gaussian-like (HGL) orthonormal eigenvectors of the discrete Fourier transform (DFT) matrix F. By exploiting the unitarity of matrix F – resulting in the orthogonality of its eigenspaces pertaining to the distinct eigenvalues – the problem decouples into finding orthonorm...

This paper is concerned with approximation properties of orthonormal mapped Chebyshev functions (OMCFs) in unbounded domains. Unlike the usual mapped Chebyshev functions which are associated with weighted Sobolev spaces, the OMCFs are associated with the usual (non-weighted) Sobolev spaces. This leads to particularly simple stiffness and mass matrices for higher-dimensional problems. The approx...

Abstract. We investigate a collection of orthonormal functions that encodes information about the continued fraction expansion of real numbers. When suitably ordered these functions form a complete system of martingale differences and are a special case of a class of martingale differences considered by R. F. Gundy. By applying known results for martingales we obtain corresponding metric theore...

In this paper, we show how to construct an orthonormal basis from Riesz by assuming that the fractional translates of a single function in core subspace multiresolution analysis form instead basis. definition analysis, intersection triviality condition follows other conditions. Furthermore, union density also under assumption Fourier transform scaling is continuous at 0. At culmination, provide...

Abstract Recent findings for optimal transport maps between distribution functions sharing the same copula show that componentwise solution is map marginal distributions. This an important discovery since in multivariate setting are difficult to find and only known a few special cases. In this paper, we extend result on common copulas by showing orthonormal transformations of variables also hav...

Introduction. The purpose of this paper is to describe an effective construction of Greene and Neumann's functions for a general class of linear, second-order partial differential equations of elliptic type in terms of a set of continuously differentiable functions, complete and orthonormal with respect to the domain considered. This result completes a previous paper by us in which an analogous...

Various results on constructing wavelets, multiwavelets and wavelet frames for periodic functions are reviewed. The orthonormal and Riesz bases as well as frames are constructed from sequences of subspaces called multiresolution analyses. These studies employ general frequency-based approaches facilitated by functions known as orthogonal splines and polyphase splines. While the focus is on the ...

The complete orthonormal sel of Walsh functions is used to generate periodic \ forms and envelope shapes for an additive synthesis electronic music device. Walsh functions, cus i ly produced In JiuiUil circuitry, can be used to generate \ of harmonic and nonhannonJC waveforms. A second Walsh function generator f the basis of a digital envelope controller which can produce a wide variety of si t...

The row-orthonormal hyperspherical coordinate (ROHC) approach to calculating state-to-state reaction cross sections and bound state levels of N-atom systems requires the use of angular momentum tensors and Wigner rotation functions in a space of dimension N - 1. The properties of those tensors and functions are discussed for arbitrary N and determined for N = 5 in terms of the 6 Euler angles in...