We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well established strategy to deal with scaling critical perturbations of dispersive PDEs, we make use Hankel transform rely on some precise Bessel functions. As complementary result, local smoothing estimate the Klein-Gordon equation same field.

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so that an is the sum of the n th and n + 1 Catalan numbers. Then the Hankel transform of {a0, a1, a2, . . .} begins 2, 5, 13, 34, . . .. Layman first conjectured in the On-Line Encyclopedia of Integer Sequences ([4], see sequence A001906) that this sequence consists of every other Fibonacci number, and subsequently Cvetković, Rajković and Ivković [2] proved this conjecture. The current paper a...

We propose to find the propagation constants of modes in layered media by means of signal identification methods. To this effect we employ Cauchy’s theorem, conformal mapping and Fast Fourier Transform (FFT) techniques to generate relevant Hankel moments, afterwards to be processed with selected signal identification algorithms. The method, terminated by a few Newton steps, provides a batch of ...

The Euler transformation is a linear sequence transformation to accelerate the convergence of an alternating series. The sequence of weights of the transformation is extended to a continuous weight function which can accelerate Fourier type integrals including Hankel transforms with a slowly convergent integrand. We show that the continuous weight function can also be used to compute the Fourie...

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...

The connection between the Bessel discrete variable basis expansion and a specific form of an orthogonal set of Jacobi polynomials is demonstrated. These so-called Zernike polynomials provide alternative series expansions of suitable functions over the unit interval. Expressing a Bessel function in a Zernike expansion provides a straightforward method of generating series identities. Furthermor...

Using some techniques developed by Dragomir and Wang in the recent paper [2] in connection to Ostrowski integral inequality, we point out some approximation results for the Henkel’s transform of absolutely continuous mapping.