Related papers: Non-Euclidean Fourier inversion on super-hyperboli…
In this note, we prove a theorem \`a la Fatou for the square root of Poisson Kernel in the context of quasi-convex cocompact discrete groups of isometries of $\delta$-hyperbolic spaces. As a corollary we show that some matrix coefficients…
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 $\alpha>1$…
We consider fractional Hartree and cubic nonlinear Schr\"odinger equations on Euclidean space $\mathbb R^d$ and on torus $\mathbb T^d$. We establish norm inflation (a stronger phenomena than standard ill-posedness) at every initial data in…
We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space $\H^n$. This enables us to find asymptotic properties of the kernel. Our starting point is the formula for its Fourier…
We present novel microlocal and injectivity analyses of ellipsoid and hyperboloid Radon transforms. We introduce a new Radon transform, $R$, which defines the integrals of a compactly supported $L^2$ function, $f$, over ellipsoids and…
In this paper, we utilize the method in Dodson-Murphy [4] to establish the radial scattering result for the focusing nonlinear Schr\"odinger equation with inverse square potential $i\pa_tu-\la u=-|u|^{p-1}u$ in the energy space…
Working to lowest non-trivial order in fermions, we consider the four-derivative order corrected Lagrangian and supersymmetry transformations of the Euclidean Bagger-Lambert-Gustavsson theory. By demonstrating supersymmetric invariance of…
We study well-posedness of degenerate mixed-type parabolic-hyperbolic equations $$ \partial_tu+\text{div}\big(f(u)\big)=\mathcal{L}[b(u)] $$ on bounded domains with general Dirichlet boundary/exterior conditions. The nonlocal diffusion…
In this paper a new class of radial basis functions based on hyperbolic trigonometric functions will be introduced and studied. We focus on the properties of their generalised Fourier transforms with asymptotics. Therefore we will compute…
We give a new and self-contained proof of a generic version of the (former) Helgason conjecture. It says that for generic spectral parameters the Poisson transform is a topological isomorphism, with the inverse given by a boundary value…
A Fourier transform from momentum space to twistor space is introduced in twistor string theory, for the first time, for the case where the twistor space is a three-dimensional real projective space, corresponding to ultra-hyperbolic…
For every natural number k we introduce the notion of k-th order convolution of functions on abelian groups. We study the group of convolution preserving automorphisms of function algebras in the limit. It turns out that such groups have…
The transverse polarization observed in the inclusive production of Lambda hyperons in the high energy collisions of unpolarized hadrons is tackled by considering a new set of spin and kT dependent quark fragmentation functions. Simple…
The aims of the reported work are to provide new insights into the quantum dot optical properties confined in an inverse of a quadratic Hellmann potential. The Schr\"odinger equation is solved using the Nikiforov-Uvarov (NU) method, in…
The paper deals about Hardy-type inequalities associated with the following higher order Poincar\'e inequality: $$ \left( \frac{N-1}{2} \right)^{2(k -l)} := \inf_{ u \in C_{c}^{\infty} \setminus \{0\}} \frac{\int_{\mathbb{H}^{N}}…
We review the basic theory of super $G$-spaces. We prove a theorem relating the action of a super Harish-Chandra pair $(G_0, \mathfrak{g})$ on a supermanifold to the action of the corresponding super Lie group $G$. The theorem was stated in…
We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to H\"ormander's support theorem for…
We prove sphere packing density bounds in hyperbolic space (and more generally irreducible symmetric spaces of noncompact type), which were conjectured by Cohn and Zhao and generalize Euclidean bounds by Cohn and Elkies. We work within the…
An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N-3) functionally independent constants of the motion. Among them, two…
We prove that a compact, intrinsically symmetric submanifold of a Euclidean space is extrinsically symmetric if and only if its maximal tori are Clifford tori in the ambient space. Moreover, we show that this result can be used to give a…