The mode-matching applications to scattering from circular and annular apertures in a thick perfectly conducting plane are reviewed. The Hankel and Weber transforms are utilized to solve the boundary-value problems of circular and annular apertures. Simple electrostatic problems are presented to illustrate the mode-matching method in terms of the Hankel and Weber transforms. Various types of We...

We study the boundedness properties of truncation operators acting on bounded Hankel (or Toeplitz) infinite matrices. A relation with the Lacey-Thiele theorem on the bilinear Hilbert transform is established. We also study the behaviour of the truncation operators when restricted to Hankel matrices in the Schatten classes. 1. Statement of results In this note we will be dealing with infinite ma...

The purpose of this study is to develop an accelerated MR parameter mapping technique. For accelerated T1 and T2 mapping, spin-echo inversion recovery and multi-echo spin echo pulse sequences were redesigned to perform undersampling along phase encoding direction. The highly missing k-space were then interpolated by using recently proposed annihilating filter based low-rank Hankel matrix approa...

The significance of the similarity theorem for the fractional Fourier transform is discussed, and the properties of self-similar functions considered. The concept of the fractional Hankel transform is developed for use in the analysis of diffraction and imaging in symmetrical optical systems. The particular case of Fresnel diffraction from a circular aperture is discussed and the effects of the...

In this paper, we present a systematic study of the various characteristics and properties some continuous discrete fractional Bessel wavelet transforms. The method is based upon theory Hankel transform.

We develop the nth order Fourier-Bessel series expansion of 1-D functions in the interval (0,α). Hence we establish the sampling theorem for a function with α-bandlimited nth order Hankel transform. The latter statement implies that the function is also Fourier transform αbandlimited. The samples’ locations are given by the roots of nth order Bessel functions. In addition, the sampling distance...

We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in “near-colliding” situations. We consider a case when the structure of the system is a-priori fixed. We transform the nonlinear part of the Prony system into a Hankel-type polynomial system. Combining this representation with a recentl...