Related papers: The nonsymmetric compositional Delta theorem

In previous papers, a generalization of the Weyl calculus was introduced in connection with the quantization of a particle moving in $\mathbb R^n$ under the influence of a variable magnetic field $B$. It incorporates phase factors defined…

In this paper, we unearth symmetries of different types of a nonlinear non-polynomial oscillator. The symmetries which we report here are adjoint-symmetries, contact symmetries and telescopic vector fields. We also obtain Jacobi last…

Let $\Omega \subseteq \mathbb{R}^d$ be open, $A$ a complex uniformly strictly accretive $d\times d$ matrix-valued function on $\Omega$ with $L^\infty$ coefficients, and $V$ a locally integrable function on $\Omega$ whose negative part is…

We study a nonlinear system of partial differential equations which describe rotating shallow water with an arbitrary constant polytropic index $\gamma $ for the fluid. In our analysis we apply the theory of symmetries for differential…

We define a family of symmetric and a family of non-symmetric polynomials in terms of vanishing conditions. These families depend on two paramters, q and t. Their main feature is that they consist of non-homogeneous polynomials. The…

An inverse problem for a nonlinear biharmonic operator is under consideration in the spirit of Isakov (1993) and Johansson-Nurminen-Salo (2023). We prove that a general nonlinear term of the $Q= Q(x,u, \nabla u, \Delta u)$ associated to a…

Building upon Dyson's fundamental 1962 article known in random-matrix theory as 'the threefold way', we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary symmetries. Important examples are…

We analyze the spectrum of the operator $\Delta^{-1} [\nabla \cdot (K\nabla u)]$, where $\Delta$ denotes the Laplacian and $K=K(x,y)$ is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral…

We present a non-uniform analogue of the classical Datko-Pazy theorem. Our main result shows that an integrability condition imposed on orbits originating in a fractional domain of the generator (as opposed to all orbits) implies polynomial…

A new proof for the completeness of the coherent states $D(\alpha )\mid f>$ for the Heisenberg Weyl group and the groups $SU(2)$ and $SU(1,1)$ is presented. Generalizations of these results and their consequences are disussed.

We give the correct prescriptions for the terms involving the inverse of the derivative of the delta function, in the Hamiltonian structures of the AKNS and DNLS systems, in order for the Jacobi identities to hold. We also establish that…

It is shown that a renormalizable nonlinear sigma model gives rise to the effective string theory proposed by Polchinski and Strominger. In the presence of long string background, the model contains massive world-sheet degrees of freedom…

This paper presents a multivariate generalization of Flajolet and Odlyzko's transfer theorem. Similarly to the univariate version, the theorem assumes $\Delta$-analyticity (defined coordinate-wise) of a function $A(z_1,\ldots,z_d)$ at a…

New supersymmetric partners of the modified Poschl-Teller and the Dirac's delta well potentials are constructed in closed form. The resulting one-parametric potentials are shown to be interrelated by a limiting process. The range of values…

We consider the semiclassical asymptotics of the sum of negative eigenvalues of the three-dimensional Pauli operator with an external potential and a self-generated magnetic field $B$. We also add the field energy $\beta \int B^2$ and we…

Poisson-Lie dualising the eta deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated lambda deformed model. In this paper we investigate…

We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums.…

We construct new families of conformally invariant differential operators acting on densities. We introduce a simple, direct approach which shows that all such operators arise via this construction when the degree is bounded by the…

In this paper, we are concerned with the weighted elliptic system \begin{equation*} \begin{cases} -\Delta u=|x|^{\beta} v^{\vartheta},\\ -\Delta v=|x|^{\alpha} |u|^{p-1}u, \end{cases}\quad \mbox{in}\;\ \Omega, \end{equation*}where $\Omega$…

We show that symmetric polynomials previously introduced by the author satisfy a certain differential equation. After a change of variables, it can be written as a non-stationary Schr\"odinger equation with elliptic potential, which is…