Related papers: Harmonic Extensions on $\mathbb{Z} \times \mathbb{…
Following a symmetrization procedure proposed recently by Nowak and Stempak, we consider the setting of symmetrized Jacobi expansions. In this framework we investigate mapping properties of several fundamental harmonic analysis operators,…
We study a time-dependent non-Hermitian extension of the Sch\"utte-Da~Provid\^encia spin-boson Hamiltonian with complex couplings. A time-dependent Dyson map containing a squeezing transformation maps the model, in an admissible bounded…
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and…
We solve the Dirichlet problem $\left.u\right|_{\mathbb{B}^n}=\varphi,$ for hyperbolic Poisson's equation $\Delta_h u=\mu$ where $\varphi\in L_1(\partial \mathbb{B}^n)$ and $\mu$ is a measure that satisfies a growth condition. Next we…
By considering the nonrelativistic limit of de-Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton-Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of…
We give improved bounds for the distortion of the Hausdorff dimension under quasisymmetric maps in terms of the dilatation of their quasiconformal extension. The sharpness of the estimates remains an open question and is shown to be closely…
Supersymmetric extensions of the 1D and 2D Swanson models are investigated by applying the conformal bridge transformation (CBT) to the first order Berry-Keating Hamiltonian multiplied by $i$ and its conformally neutral enlargements. The…
We show, by applying discrete weighted norm inequalities and the Rubio de Francia algorithm, that the discrete Hilbert transform and discrete Riesz potential are bounded on variable $\ell^{p(\cdot)}(\mathbb{Z})$ spaces whenever the discrete…
We show that the biharmonic Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis…
A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al., and later generalized to the Riemannian manifold setting in Duruisseaux and Leok. This variational framework was…
For odd dimensional Poincar\'e-Einstein manifolds $(X^{n+1},g)$, we study the set of harmonic $k$-forms (for $k<\ndemi$) which are $C^m$ (with $m\in\nn$) on the conformal compactification $\bar{X}$ of $X$. This is infinite dimensional for…
Within Bishop-style constructive mathematics we study the classical McShane-Whitney theorem on the extendability of real-valued Lipschitz functions defined on a subset of a metric space. Using a formulation similar to the formulation of…
We propose a monotone discretization for the integral fractional Laplace equation on bounded Lipschitz domains with the homogeneous Dirichlet boundary condition. The method is inspired by a quadrature-based finite difference method of Huang…
We devise fast and provably accurate algorithms to transform between an $N\times N \times N$ Cartesian voxel representation of a three-dimensional function and its expansion into the {ball harmonics}, that is, the eigenbasis of the…
We study compact polyhedral surfaces as Riemann surfaces and their discrete counterparts obtained through quadrilateral cellular decompositions and a linear discretization of the Cauchy-Riemann equation. By ensuring uniformly bounded…
Given a densely defined and closed operator $A$ acting on a complex Hilbert space $\mathcal{H}$, we establish a one-to-one correspondence between its closed extensions and subspaces $\mathfrak{M}\subset\mathcal{D}(A^*)$, that are closed…
Maps between Riemannian manifolds which are submersions on a dense subset, are studied by means of the eigenvalues of the pull-back of the target metrics, the first fundamental form. Expressions for the derivatives of these eigenvalues…
We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to $\mathbb{Z}_2^d$. Noteworthy, we admit negative values of the…
A well known tool in conventional (von Neumann) quantum mechanics is the self-adjoint extension technique for symmetric operators. It is used, e.g., for the construction of Dirac-Hermitian Hamiltonians with point-interaction potentials.…
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…