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The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators…
A family of discrete Schroedinger operators is investigated through scattering theory. The continuous spectrum of these operators exhibit changes of multiplicity, and some of these operators possess resonances at thresholds. It is shown…
The spherical tensor gradient operator ${\mathcal{Y}}_{\ell}^{m} (\nabla)$, which is obtained by replacing the Cartesian components of $\bm{r}$ by the Cartesian components of $\nabla$ in the regular solid harmonic ${\mathcal{Y}}_{\ell}^{m}…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
We calculate the Wigner function for charged spin-1 particles in inhomogeneous classical electromagnetic fields, going to first order in a power series in $\hbar$. The Boltzmann equation for the scalar distribution function obtained from…
In hadron spectrum physics, the partial wave analysis is a primary method used to extract properties of hadronic resonances. The covariant orbital-spin coupling scheme holds unique advantages over other partial wave methods due to its…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
An explicit formula for the wave operators associated with Schroedinger operators on the discrete half-line is deduced from their stationary expressions. The formula enables us to understand the wave operators as one dimensional…
The analytical relations in position, momentum and four-dimensional spaces are established for the expansion and one-range addition theorems of relativistic complete orthonormal sets of exponential type spinor wave functions and Slater…
We apply the Hilbert series to extend the gravitational action for a scalar field to a complete, non-redundant basis of higher-dimensional operators that is quadratic in the scalars and the Weyl tensor. Such an extension of the action fully…
We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…
We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with a finite spectrum. Our result extends the Schur-Horn theorem from a finite dimensional setting to an infinite dimensional Hilbert space analogous to…
Scalar-tensor theories are one of the most natural and well-constrained alternative theories of gravity, while still allowing for significant deviations from general relativity. We present the equations of motion of nonspinning compact…
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
This paper deals with a certain class of second-order conformally invariant operators acting on functions taking values in particular (finite-dimensional) irreducible representations of the orthogonal group. These operators can be seen as a…
On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the…
The ladder operators in harmonic oscillator are a well-known strong tool for various problems in physics. In the same sense, it is sometimes expected to handle the problems of repulsive harmonic oscillator in a similar way to the ladder…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
The Schur orthogonality relations are a cornerstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new, readily verifiable condition on the skeletal data for deciding whether a given…
Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded domains, focusing on those with integrable kernels having…