Related papers: Conformally Invariant Operators via Curved Casimir…
We consider the classical problem of the construction of invariant tori exploiting suitable Hamiltonian normal forms. This kind of approach can be translated by means of the Lie series method into explicit computational algorithms, which…
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations. It is effective for both continuous and discrete models. The first operator of the Lax pair corresponding to a given nonlinear equation is found…
Inversion of operators is a fundamental concept in data processing. Inversion of linear operators is well studied, supported by established theory. When an inverse either does not exist or is not unique, generalized inverses are used. Most…
There is constructed and considered the extension of classical Diriclet operator corresponding to uniformly log-concave measure in the space of symmetric differential forms. Sufficient conditions for its essential self-adjointness in…
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras $sp(n,1)$. Our choice of these algebras is motivated by the fact that they belong to a…
We derive extrinsic GJMS operators and $Q$-curvatures associated to a submanifold of a conformal manifold. The operators are conformally covariant scalar differential operators on the submanifold with leading part a power of the Laplacian…
We construct Rankin-Cohen type differential operators on Hermitian modular forms of signature $(n,n)$. The bilinear differential operators given here specialize to the original Rankin-Cohen operators in the case $n=1$, and more generally…
We introduce a search algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. To demonstrate the algorithm, we look at two classes of examples: (1) the model filiform Lie algebras and…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
A complete classification of linear differential operators possessing finite-dimensional invariant subspace with a basis of monomials is presented.
Let ${\cal F}_\lambda$ be the space of tensor densities on ${\bf R}^n$ of degree $\lambda$ (or, equivalently, of conformal densities of degree $-\lambda{}n$) considered as a module over the Lie algebra $so(p+1,q+1)$. We classify…
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…
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.
We consider a generic curved non-commutative torus extending the notion of conformally deformed non-commutative torus from \cite{Connes-Tretkoff}. In general, a curved non-commutative torus is no longer represented by a spectral triple, not…
We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a…
We compute conformally covariant actions and operators for tensors with mixed symmetries in arbitrary dimension $d$. Our results complete the classification of conformal actions that are quadratic on arbitrary tensors with three indices,…
Superconformal methods are useful to build invariant actions in supergravity. We have a good insight in the possibilities of actions that are at most quadratic in spacetime derivatives, but insight in general higher-derivative actions is…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
Motivated by PDE-learning, we give a classifying space for nonlinear operators on simply connected spaces with constant curvature which are also equivariant under the action of the isometry group. The nonlinear operators we are considering…