Related papers: Symmetry breaking differential operators, the sour…
We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We discuss ladder operators for this variable, and confirm that they obey the commutation…
In this paper, we consider periodic boundary value problems for differential equations whose coefficients are trigonometric polynomials. We construct the spaces of generalized functions, where such problems have solutions. In particular,…
We identify Melrose's suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space $\R$. For a general algebra of parametric pseudodifferential operators,…
In this survey article we discuss the question: to what extent is an algebraic variety determined by its ring of differential operators? In the case of affine curves, this question leads to a variety of mathematical notions such as the Weyl…
We develop an operator approach to the integration of linear differential equations based on intertwining relations between differential operators. Conditions for the existence of intertwining operators are obtained, and it is shown that,…
We define the braided differential algebras which can be interpreted as quantization of the differential operator algebra defined on some algebraic varieties supplied with the action of the group GL(m). The algebra is generated by right…
We consider the cotriple resolution of algebras over operads in differential graded modules. We focus, to be more precise, on the example of algebras over the differential graded Barratt-Eccles operad and on the example of commutative…
In this article we consider 2-dimensional surfaces. We define some new operators which enable us to evaluate quantities of the surface, such invariants, in a more systematic way.
We propose a generalization of the notion of ${\bf R}$-split mixed Hodge structure by defining a ${\bf R}$-splitting level for mixed Hodge structures. This is a discrete invariant taking values in positive integers and equal to 0 for ${\bf…
The Calogero model is a one-dimensional quantum integrable system with inverse-square long-range interactions confined in an external harmonic well. It shares the same algebraic structure with the Sutherland model, which is also a…
We propose a splitting method for solving an equilibrium problem involving the sum of two bifunctions satisfying standard conditions. We prove that this problem is equivalent to find a zero of two appropriate maximally monotone operators.…
We consider bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class, $BS_{\rho, \rho}^m$, $m \in \mathbb{R}$, $0 \leq \rho < 1$. The aim of this paper is to discuss low regularity conditions for symbols to…
The method to solve inhomogeneous linear differential equations that is usually taught at school relies on the fact that the right hand side function is the product of a polynomial and an exponential and that the linear spaces of those…
We study the space of local operators in the sinh-Gordon model in the framework of the bootstrap form factor approach. Our final goal is to identify the operators obtained by solving bootstrap equations with those defined in terms of the…
The field equations of the auxiliary fields are nonlinear and free of derivatives. Hence, it is argued, a Legendre transform to generate the 1PI Generating Functionals is not correct for the auxiliary fields. A corrected formulation of the…
We discuss Sekiguchi-type differential operators, their eigenvalues, and a generalization of Andrews-Goulden-Jackson formula. These will be applied to extract explicit formulae involving shifted partitions and hook lengths.
In this paper we classify and construct differential symmetry breaking operators $\mathbb{D}$ from a line bundle over the real projective space $\mathbb{R}\mathbb{P}^n$ to a vector bundle over $\mathbb{R}\mathbb{P}^{n-1}$. We further…
The classical Rankin-Cohen brackets are bi-differential operators from $C^\infty(\mathbb R)\times C^\infty(\mathbb R)$ into $ C^\infty(\mathbb R)$. They are covariant for the (diagonal) action of ${\rm SL}(2,\mathbb R)$ through principal…
We consider an overdetermined problem of Serrin-type with respect to an operator in divergence form with piecewise constant coefficients. We give sufficient condition for unique solvability near radially symmetric configurations by means of…
We construct a family of bilinear differential operators which satisfy certain gauge properties. These operators can be naturally associated with $q$-deformations of classical integrable hierarchies. In particular, we consider the case when…