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 transform the nonlinear part of the Prony system into a Hankel-type polynomial system. Combining this representation with a recently discovered “decimation” technique, we present an algorithm which appl...

We derive completeness criteria for sequences of functions of the form f(xλn), where λn is the nth zero of a suitably chosen entire function. Using these criteria, we construct complete nonorthogonal systems of FourierBessel functions and their q-analogues, as well as other complete sets of qspecial functions. We discuss connections with uncertainty principles over q-linear grids and the comple...

We describe an approach to determining both the angular and the radial modal content of a scalar optical beam in terms of optical angular momentum modes. A modified Mach-Zehnder interferometer that incorporates a spatial rotator to determine the angular modes and an optical realization of the fractional Hankel transform (fHT) to determine the radial modes is analyzed. Varying the rotation angle...

This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. The little Hankel operators on these Bergman spaces are also considered. Next, a study is made of Carleson embeddings in the right half-plane induced by taking the Laplace transform of functions defined on the positive h...

An efficient automatic quadrature procedure is developed for numerically computing the integrals 0 , where the function is smooth and nonoscillatory at infinity and is the Bessel functions of order ν =1,0 and 1/4. The procedure involves the use of an automatic integration scheme of modified FFT used for evaluating Fourier integrals and product type integration, and the modified W-transformation...

More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated D...

The vortex coronagraph is a transparent phase-based coronagraph which imprints an eilθ phase ramp (or screw dislocation) on the point spread function (PSF) of the telescope+instrument. l is called the topological charge of the vortex, and quantifies the number of times the phase goes through 2π radians. For the vortex to be an efficient coronagraph, the topological charge has to be a non-zero e...

In the theory for continuous-time linear systems, the system Hankel operator plays an important role in a number of realization problems ranging from providing an abstract notion of state to yielding tests for state space minimality and algorithms for model reduction. But in the case of continuous-time nonlinear systems, Hankel theory is considerably less developed beyond a well known Hankel ma...

 sinx x if x 6= 0 1 otherwise This function is important in many areas of computing science, approximation theory, and numerical analysis. For example, it is used in interpolation and approximation of functions, approximate evaluation of transforms (e.g. Hilbert, Fourier, Laplace, Hankel, and Mellon transforms as well as the fast Fourier transform). It is used in finding approximate solutions ...

The algorithm of discrete wavelet transform is developed to achieve the integrity authentication of color image contents through embedding watermarking. Firstly, a new watermarking image is generated with the XOR between the original binary watermarking and the image which is processed with Hankel transform. When the watermark is embedded, the original image color is converted first and the bri...