We consider orthonormal expansions where the basis functions are governed by some free parameters. If the basis functions adhere to a certain differential or difference equation, then an expression can be given for a specific enforced convergence rate criterion as well as an upper bound for the quadratic truncation error. This expression is a function of the free parameters and some simple sign...

We consider the space Pn of orthogonal polynomials of degree n on the unit disc for a general radially symmetricweight function.We show that there exists a single orthogonal polynomialwhose rotations through the angles j n+1 , j = 0, 1, . . . , n forms an orthonormal basis for Pn, and compute all such polynomials explicitly. This generalises the orthonormal basis of Logan and Shepp for the Lege...

For the space of two identical systems of arbitrary dimensions, we introduce a continuous family of bases with the following properties: i) the bases are orthonormal, ii) in each basis, all the states have the same values of entanglement, and iii) they continuously interpolate between the product basis and the maximally entangled basis. The states thus constructed may find applications in many ...

Abstract In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], an electron moving plane uniform external magnetic and electric fields which possesses both discrete continuous spectra. The eigenfunctions are realized as orthonormal basis suitable Hilbert space appropriate for building the states. These latter achieved context where ...

Algorithms for designing a mother wavelet ( ) such that it matches a signal of interest and such that the family of wavelets 2 ( 2) (2 ) forms an orthonormal Riesz basis of ( ) are developed. The algorithms are based on a closed form solution for finding the scaling function spectrum from the wavelet spectrum. Many applications of signal representation, adaptive coding and pattern recognition r...