The Green function of Mumford-Shah functional in the absence of discontinuities is known to be a modified Bessel function of the second kind and zero degree. Such a Bessel function is regularized here and used as a filter for feature extraction. It is demonstrated in this paper that a Bessel filter does not follow the scale space smoothing property of bounded linear filters such as Gaussian fil...

Let the Bessel number of the second kind B(n, k) be the number of set partitions of [n] into k blocks of size one or two, and let the Bessel number of the first kind b(n, k) be the coefficient of x in −yn−1(−x) , where yn(x) is the nth Bessel polynomial. In this paper, we show that Bessel numbers satisfy two properties of Stirling numbers: The two kinds of Bessel numbers are related by inverse ...

Small parameter power series expansions for both radial and angular Mathieu functions are derived. The expansions are valid for all integer orders and apply the Stratton-Morse-Chu normalization. Three new contributions are provided: (1) explicit power series expansions for the radial functions, which are not available in the literature; (2) improved convergence rate of the power series expansio...

Using a Bessel generalized translation, we obtain an analog of Titchmarsh's theorem for the Bessel transform for functions satisfying the Lipschitz condition in the space $mathrm{L}_{p,alpha}(mathbb{R}_{+})$, where $alpha>-frac{1}{2}$ and $1

Abstract. Block sequences with respect to frames in Hilbert spaces have been defined. Examples have been provided to show that a block sequence with respect to a given frame may not even be a Bessel sequence. Also, a necessary and sufficient condition under which a block sequence with respect to a frame is a frame has been given. Further, applications of block sequences to obtain Fusion frames ...

Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...

We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.

In this paper we investigate Bessel sequences in the space L2(R s), in Sobolev spaces Hμ(Rs) (μ > 0), and in Besov spaces B μ p,p(R s) (1 p ∞). For each j ∈ Z, let Ij be a countable index set. Let (ψj,α)j∈Z, α∈Ij be a family of functions in L2(R). We give some sufficient conditions for the family to be a Bessel sequence in L2(R s) or Hμ(Rs). The results obtained in this paper are useful for the...

A new method of generating the Bessel functions and ratios of Bessel functions necessary for Mie calculations is presented. Accuracy is improved while eliminating the need for extended precision word lengths or large storage capability. The algorithm uses a new technique of evaluating continued fractions that starts at the beginning rather than the tail and has a built-in error check. The conti...

Recently, the use of Bessel beams in evaluating the possibility of using them for a new generation of ground penetrating radar systems has been considered. Therefore, an analysis of the propagation of Bessel beams in conducting media is worthwhile. We present here an analysis of this type. Specifically, for normal incidence we analyze the propagation of a Bessel beam coming from a perfect diele...