Using normalized Hermite functions, we construct bases in the space of square integrable functions on unit circle (L2(C)) and l2(Z), which are related to each other by means Fourier transform discrete transform. These relations unitary. The construction orthonormal requires use Gramm–Schmidt method. On both spaces, have provided ladder operators with same properties as for one-dimensional quant...

In this paper, model sets for continuous{time linear time invariant systems that are spanned by xed pole orthonormal bases are investigated. These bases gen-eralise the well known Laguerre and Kautz bases. It is shown that the obtained model sets are complete in all of the Hardy spaces H p ((); 1 p < 1 and the right half plane algebra A(() provided that a mild condition on the choice of basis p...

Modelling randomness in shape data, for example, the evolution of shapes organisms biology, requires stochastic models shapes. This paper presents a new model based on description as functions Sobolev space. Using an explicit orthonormal basis reference frame noise, is independent parameterisation mesh. We define model, explore its properties, and illustrate examples evolutions using resulting ...

We exhibit the necessary range for which functions in Sobolev spaces L p s $L^s_p$ can be represented as an unconditional sum of orthonormal spline wavelet systems, such Battle–Lemarié wavelets. also consider natural extensions to Triebel–Lizorkin spaces. This builds upon, and is a generalization of, previous work Seeger Ullrich, where analogous results were established Haar system.

We solve the joint open problems of photon localization and single-photon wave functions in the context of spontaneous emission from an excited atom in free space. Our wave functions are well-defined members of a discrete orthonormal function set. Both the degree and shape of the localization are controlled by entanglement mapping onto the atom wave function, even though the atom is remote from...

This study considers a class of double finite Hankel transforms that describes the transmission of a vortex optical signal through a two-lens system with limited aperture radii in the object and spectral flats. The eigenfunctions of the given transform are calculated for different orders of vortex m. The functions obtained are an orthonormal system of functions, which can help expand an unspeci...