We show here that a certain sequence of polynomials arising in the study of S2 m-quasi invariants satisfies a 3-term recursion. This leads to the discovery that these polynomials are closely related to the Bessel polynomials studied by Luc Favreau. This connection reveals a variety of combinatorial properties of the sequence of Baker–Akhiezer functions for S2. In particular we obtain in this ma...

We construct a system of interacting two-sided Bessel processes on the unit interval and show that the associated empirical measure process converges to the Wasserstein Diffusion [27], assuming that Markov uniqueness holds for the generating Wasserstein Dirichlet form. The proof is based on the variational convergence of an associated sequence of Dirichlet forms in the generalized Mosco sense o...

We study Galton-Watson branching processes conditioned on the total progeny to be n which are scaled by a sequence cn tending to innnity as o(p n). It is shown that this process weakly converges to the totallocal time of a two-sided three-dimensional Bessel process. This is done by means of characteristic functions and a generating function approach.

Active technologies can enable room acoustic diffusers to operate over a wider bandwidth than passive devices, by extending the bass response. Active impedance control can be used to generate surface impedance distributions which cause wavefront dispersion, as opposed to the more normal absorptive or pressure-cancelling target functions. This paper details the development of two new types of ac...

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 ...