Related papers: Funk-Minkowski transform and spherical convolution…
We describe the quantum sphere of Podle\'{s} for $c=0$ by means of a stereographic projection which is analogous to that which exhibits the classical sphere as a complex manifold. We show that the algebra of functions and the differential…
Quantum hamiltonian reduction is a fundamental tool of conformal field theory and vertex algebra representation theory. It has traditionally been applied to study highest-weight modules. On the other hand, inverse quantum hamiltonian…
A space curve is determined by conformal arc-length, conformal curvature, and conformal torsion, up to M\"obius transformations. We use the spaces of osculating circles and spheres to give a conformally defined moving frame of a curve in…
Given a real valued function on R^n we study the problem of recovering the function from its spherical means over spheres centered on a hyperplane. An old paper of Bukhgeim and Kardakov derived an inversion formula for the odd n case with…
In this paper, we introduce isoparametric functions and isoparametric hypersurfaces in Finsler manifolds and give the necessary and sufficient conditions for a transnormal function to be isoparametric. We then prove that hyperplanes,…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
The main aim of the present paper is to establish an integral transform connecting spherical analysis on harmonic NA groups to that of odd dimensional real hyperbolic spaces. Moreover, certain interesting integral identities for the Gauss…
The result of Guan and Ma (Invent. Math. 151 (2003)) states that if $\phi^{-1/k} : \mathbb{S}^n \to (0,\infty)$ is spherically convex, then $\phi$ arises as the $\sigma_k$ curvature (the $k$-th elementary symmetric function of the principal…
A symmetric bilinear form on a certain subspace $\widehat{\mathbb T}^{\bf b}$ of a completion of the Fock space $\mathbb T^{{\bf b}}$ is defined. The canonical and dual canonical bases of $\widehat{\mathbb T}^{\bf b}$ are dual with respect…
By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Humbert hypergeometric functions $\Phi_1 $, $\Phi_2 $, $\Phi_3 $, $\Psi_1 $,…
In \cite{LX}, the first author and the third author introduced and studied the horospherical $p$-Minkowski problem for smooth horospherically convex domains in hyperbolic space. In this paper, we introduce and solve the discrete…
A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.
The Hopf algebra of renormalization in quantum field theory is described at a general level. The products of fields at a point are assumed to form a bialgebra B and renormalization endows T(T(B)^+), the double tensor algebra of B, with the…
Report II is concerned with the extended results of distance function wavelets (DFW). The fractional DFW transforms are first addressed relating to the fractal geometry and fractional derivative, and then, the discrete Helmholtz-Fourier…
The possibility of solving the Bethe-Salpeter Equation in Minkowski space, even for fermionic systems, is becoming actual, through the applications of well-known tools: i) the Nakanishi integral representation of the Bethe-Salpeter…
We consider the $\alpha$-sine transform of the form $T_\alpha f(y)=\int_0^\infty\vert\sin(xy)\vert^\alpha f(x)dx$ for $\alpha>-1$, where $f$ is an integrable function on $\mathbb{R}_+$. First, the inversion of this transform for $\alpha>1$…
In this talk, we show how the Connes-Kreimer Hopf algebra morphism can be extended when taking into account the wave-function renormalization. This leads us to a semi-direct product of invertible power series by formal diffeomorphisms.
The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz…