Related papers: Recovering Functions from the Spherical Mean Trans…
In this paper, we extend the iterative expression for the generalized spherical functions associated to the root systems of type $A$ previously obtained beyond regular elements. We also provide the corresponding expression in the flat case.…
In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in…
We explore linear redshift distortions in wide angle surveys from the point of view of symmetries. We show that the redshift space two-point correlation function can be expanded into tripolar spherical harmonics of zero total angular…
In the present paper, we introduced the extended bicomplex plane $\bar{\mathbb{T}}$, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about the convergence of the sequences of…
The numerical evaluation of an individual Bessel or Hankel function of large order and large argument is a notoriously problematic issue in physics. Recurrence relations are inefficient when an individual function of high order and argument…
This paper describes an approach for fitting an immersed submanifold of a finite-dimensional Euclidean space to random samples. The reconstruction mapping from the ambient space to the desired submanifold is implemented as a composition of…
In studies of smooth maps with good differential topological conditions such as immersions, embeddings, Morse functions and their higher dimensional versions including fold maps and application to geometry, especially algebraic and…
It is known that the Funk transform (the Funk-Radon transform) is invertible in the class of even (symmetric) continuous functions defined on the unit 2-sphere S^2. In this article, for the reconstruction of f from C(S^2) (can be non-even),…
Many real-life signals are defined on spherical domains, in particular in geophysics and physics applications. In this work, we tackle the problem of extending the iterative filtering algorithm, developed for the decomposition of…
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…
The article suggests a new approach what is called a consistency method for the inversion of the spherical Radon transform in 2D with detectors on a line. It is known that there is not an exact inversion formula in 2D. By means of the…
We develop a new point of view to introduce families of functions, which can be identified as generalization of the ordinary trigonometric or hyperbolic functions. They are defined using a procedure based on umbral methods, inspired to the…
Recently, Hong, Mertens, Ono and Zhang proved a conjecture of C\u{a}ld\u{a}raru, He, and Huang that expresses the Taylor series of the modular $j$-function around the elliptic points $i$ and $\rho=e^{\pi i/3}$ as rational functions arising…
We study the problem of recovering the initial data (f, 0) of the standard wave equation from the Neumann trace (the normal derivative) of the solution on the boundary of convex domains in arbitrary spatial dimension. Among others, this…
Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements of the antidual space $\Phi^\times$ in a convenient Gelfand triplet…
In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K{\i}ymaz O. A certain generalized Pochhammer symbol and its…
Let $\lambda$ be a real number with $-\pi/2<\lambda<\pi/2.$ In order to study $\lambda$-spirallike functions, it is natural to measure the angle according to $\lambda$-spirals. Thus we are led to the notion of $\lambda$-argument. This fits…
Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…
In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind and express it in terms of the Lerch function. There are some useful results relating double…
We determine closed and compact expressions for the epsilon-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations. This epsilon-expansion is…