Related papers: Discrete pseudo-differential operators and applica…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
Differential operators on Schwartz distributions conventionally are defined as the transpose of differential operators on functions with compact support. They do not exhaust all differential operators. We follow algebraic formalism of…
Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual…
In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive…
A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostrowski's method for solving systems of nonlinear equations…
In this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain a new explicit parametrisation of torsion free rank one sheaves on projective irreducible…
We initiate a systematic study of natural differential operators in Riemannian geometry whose leading symbols are not of Laplace type. In particular, we define a discrete leading symbol for such operators which may be computed pointwise, or…
The correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras. New families of…
This paper presents a general definition of pseudo-differential operators of type $1,1$; the definition is shown to be the largest one that is both compatible with negligible operators and stable under vanishing frequency modulation.…
This paper has been withdrawn by the authors. A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those…
This paper demonstrates the stability of the global regularity for a class of pseudo-differential operators under lower-order perturbations. We establish that if an operator has a globally hypoelliptic symbol, its global regularity (in the…
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie…
A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those pseudodifferential operators act continuously on…
Dissipation and irreversibility are central to most physical processes, yet they lead to non-unitary dynamics that are challenging to realise on quantum processors. High-order operator splitting is an attractive approach for simulating…
We introduce the forward (backward) gH-difference operator of interval sequences, and establish some new discrete Opial type inequalities for interval-valued functions. Further, we obtain generalizations of classical discrete Opial type…
This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…
We study infinite order differential operators acting in the spaces of exponential type entire functions. We derive conditions under which such operators preserve the set of Laguerre entire functions which consists of the polynomials…
We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary…
Hamiltonian Operator Inference has been introduced in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. This approach…
In this work we characterise the H\"ormander classes $\symbClassOn{m}{\rho}{\delta}{\group,\textnormal{H\"or}}$ on the open manifold $\group = (-1,1)^n$. We show that by endowing the open manifold $\group = (-1,1)^n$ with a group structure,…