PROOF. Apply Theorem J for the case w==r. We obtain for gr an expression which differs from the one just written only in the fact that the terms Brtr+ifr+i+Brtr+2fr+2+ • • • +Br,nfn are missing from its numerator. But the coefficients J3r,, = 0 when r<s. Hence the two expressions are equal. REMARK. The generalization of the method to orthonormalization with respect to a general norming or weigh...

We provide a detailed treatment of Weyl–Titchmarsh theory for half-lattice and full-lattice CMV operators and discuss their systems of orthonormal Laurent polynomials on the unit circle, spectral functions, variants of Weyl–Titchmarsh functions, and Green’s functions. In particular, we discuss the corresponding spectral representations of half-lattice and full-lattice CMV operators.

We report an infinite number of orthonormal wave functions bases for the quantum problem a free particle in presence applied external magnetic field. Each set (basis) is labeled by integer $p$, which fluxons trapped unit cell. These are suitable to describe particles whose probability density periodic and defines lattice position space. The present unveils fractional effects since cell independ...

We provide a detailed treatment of Weyl–Titchmarsh theory for half-lattice and full-lattice CMV operators and discuss their systems of orthonormal Laurent polynomials on the unit circle, spectral functions, variants of Weyl–Titchmarsh functions, and Green’s functions. In particular, we discuss the corresponding spectral representations of half-lattice and full-lattice CMV operators.

Starting from the standard harmonic oscillator basis, we construct new sets of orthonormal wave functions with non-Gaussian asymptotic spatial dependence. These new wave functions can be used to study at numerical level two-body bound systems like mesons and baryons within quark-diquark models. Generalized hyperradial functions for three-quark models are also studied. c © Electronic Journal of ...

We construct smooth nonseparable compactly supported refinable functions that generate multiresolution analyses on L2(R), d > 1. Using these refinable functions we construct smooth nonseparable compactly supported orthonormal wavelet systems. These systems are nonseparable, in the sense that none of its constituent functions can be expressed as the product of two functions defined on lower dime...

One of the main aims of this paper is to bridge the gap between two branches of mathematics, special functions and wavelets. This is done by showing how special functions can be used to construct orthonormal wavelet bases in a multiresolution analysis setting. The construction uses hypergeometric functions of one and two variables and a generalization of the latter, known as Kampé de Fériet fun...