Related papers: Application of the Wavelet Transform with a Piecew…
The purpose of this paper is to represent the integral Hankel transform as a series. If one uses B-spline wavelet this series is a linear combination of the hypergeometrical functions. Numerical evaluation of the test function with known…
The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind. The result is the exact analytical representation as the series of the Bessel and Struve functions multiplied by the…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
We use a degeneration of the 1D double affine Hecke algebra and the Dunkl operator to study systematically nonsymmetric Bessel functions and their truncations.
We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…
In this work, we introduce bicomplex Bessel function and analyze its region of convergence. Important properties of the bicomplex Bessel function, such as recurrence relations, integral representations, differential relations are explored.…
The article discusses the fractional powers of the Bessel operator and their numerical implementation. An extensive literature is devoted to the study of fractional powers of the Laplace operator and their applications. Such degrees are…
A Green's function based solver for the modified Bessel equation has been developed with the primary motivation of solving the Poisson equation in cylindrical geometries. The method is implemented using a Discrete Hankel Transform and a…
In this paper, we extend the concept of continuous Bessel wavelet transform in $L^p$-space and derived the Parseval's as well as the inversion formulas. By using Bessel wavelet coefficients we characterized the Besov- Hankel space.
We study reflectionless properties at the boundary for the wave equation in one space dimension and time, in terms of a well-known matrix that arises from a simple discretisation of space. It is known that all matrix functions of the…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two…
Mellin transform is used to evaluate an integral involving the product of four Bessel functions and a power. Using this method the result is obtained in terms of generalized hypergeometric functions $_{6}F_{5}$.
In this paper, on the complex field $\mathbb{C}$, we prove two integral formulae for the Hankel-Mellin transform and the double Fourier-Mellin transform of Bessel functions, both resulting the hypergeometric function. As two applications,…
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…
Using Bauer's expansion and properties of spherical Bessel and Legender functions, we deduce a new transform and briefly indicate its use.
Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…
We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from…
This paper describes the partial wave expansion and integral representation of Bessel beams in free space and in the presence of dispersion. The expansion of the Bessel beam wavepacket with constant spectrum is obtained as well.…
We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of…