Let W (ψ; x, y) be the wideband ambiguity function. It is obtained in this note that y− α+2 2 W (ψ;x, y)(α > −1) is SO(2)-invariant if and only if the Fourier transform of ψ is a Laguerre function.

We present a direct proof of a known result that the Hardy operator Hf(x) = 1 x R x 0 f(t) dt in the space L = L2(0,∞) can be written as H = I − U , where U is a shift operator (Uen = en+1, n ∈ Z) for some orthonormal basis {en}. The basis {en} is constructed by using classical Laguerre polynomials. We also explain connections with the Euler differential equation of the first order y′− 1 x y = ...

We consider the compressive wave for the modified Korteweg–de Vries equation with background constants c > 0 for x→ −∞ and 0 for x→ +∞. We study the asymptotics of solutions in the transition zone 4ct− εt < x < 4ct − βt ln t for ε > 0, σ ∈ (0, 1), β > 0. In this region we have a bulk of nonvanishing oscillations, the number of which grows as εt ln t . Also we show how to obtain Khruslov–Kotlyar...

A unified approach is presented for the synthesis of continuous-time fractional orthogonal bases including Laguerre-like, Kautz-like and the GeneralizedOrthogonal-Basis-like (GOB-like) bases. They extend the definitions of their rational counterpart to fractional differentiation orders. Modes can either be chosen to be real or by pairs complex conjugate. Completeness of fractional Laguerre-like...

In this paper, we investigate the mixed Laguerre-Legendre interpolation approximation and its application. Some approximation results are established. A mixed Laguerre-Legendre pseudospectral scheme is constructed for incompressible fluid flow in an infinite strip. Its stability and convergence are proved. Numerical results show the efficiency of this new approach.

A pair of dual frames with almost exponentially localized elements (needlets) are constructed on R+ based on Laguerre functions. It is shown that the Triebel–Lizorkin and Besov spaces induced by Laguerre expansions can be characterized in terms of respective sequence spaces that involve the needlet coefficients. © 2008 Elsevier Inc. All rights reserved.

In this paper, we investigate a specific wave equation which generates the pre-Laguerre system, and prove that the pre-Laguerre system is related to the solution of the partial differential equation with some initial conditions. © 2013 Elsevier Ltd. All rights reserved.

In this paper, a simpli ed algorithm for constructing an internally balanced realization of a Laguerre network model is presented. Both continuous-time and discrete-time cases are treated in a uni ed framework. The algorithm does not require the computation of controllability and observability grammians, which makes it highly eÆcient, compared to existing procedures. An example is given to illu...

We describe the spectral statistics of the first finite number of eigenvalues in a newly-forming band on the hardedge of the spectrum of a random Hermitean matrix model. It is found that in a suitable scaling regime, they are described by the same spectral statistics of a finite-size Laguerre-type matrix model. The method is rigorously based on the Riemann-Hilbert analysis of the corresponding ...

In Class-D Power Amplifiers (CDPAs), the power supply noise can intermodulate with the input signal, manifesting into power-supply induced intermodulation distortion (PS-IMD) and due to the memory effects of the system, there exist asymmetries in the PS-IMDs. In this paper, a new behavioral modeling based on the Elman Wavelet Neural Network (EWNN) is proposed to study the nonlinear distortion o...