In this article, we prove a restriction theorem for the Fourier–Hermite transform and obtain Strichartz estimate system of orthonormal functions Hermite operator $$H=-\Delta +|x|^2$$ on $${\mathbb {R}}^n$$ as application. Further, show optimal behavior constant in limit large number functions.

A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform on the real line is proved. To this end we state, in terms of Bessel functions, an orthonormal system which is complete in L2((−1, 1), |x|2α+1 dx). This orthonormal system is a generalization of the classical exponential system defining Fourier series.

Abstract We give a proof of the Lieb–Thirring inequality on kinetic energy orthonormal functions by using microlocal technique, in which uncertainty and exclusion principles are combined through use Besicovitch covering lemma.

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalized orthonormal basis functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and ...

The method of Dubuc and Deslauriers on symmetric interpolatory subdivision is extended to study the relationship between interpolation processes and wavelet construction. Refinable and interpolatory functions are constructed in stages from B-splines. Their method constructs the filter sequence (its Laurent polynomial) of the interpolatory function as a product of Laurent polynomials. This provi...