Related papers: Singular reduction operators in two dimensions
Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…
This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar…
In this paper we develop a new approach for studying differential operators of an isolated singularity graded hypersurface ring $R$ defining a surface in affine three-space over a field of characteristic zero. With this method, we construct…
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…
Using an extension of the H\"ormander product of distributions, we obtain an intrinsic formulation of one-dimensional Schr\"odinger operators with singular potentials. This formulation is entirely defined in terms of standard {\it Schwartz}…
The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of…
We study the quantitative unique continuation property of some higher order elliptic operators. In the case of $P=(-\Delta)^m$, where $m$ is a positive integer, we derive lower bounds of decay at infinity for any nontrivial solutions under…
One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized…
Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…
Operator monotone functions, introduced by Lowner in 1934, are an important class of real-valued functions. They arise naturally in matrix and operator theory and have various applications in other branches of mathematics and related…
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
We present the explicit formulae, describing the structure of symmetries and formal symmetries of any scalar (1+1)-dimensional evolution equation. Using these results, the formulae for the leading terms of commutators of two symmetries and…
We define a class of discrete operators that, in particular, include the delta and nabla fractional operators.
he Singular Manifold Method is presented as an excellent tool to study a 2+1 dimensional equation in despite of the fact that the same method presents several problems when applied to 1+1 reductions of the same equation. Nevertheless these…
A study of the superconformal covariantization of superdifferential operators defined on $(1|1)$ superspace is presented. It is shown that a superdifferential operator with a particular type of constraint can be covariantized only when it…
We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to…
We investigate N-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer n, N=2n supercharges are explicitly constructed and a class of point singularities compatible with…
We obtain a Bloom-type characterization of the two-weighted boundedness of iterated commutators of singular integrals. The necessity is established for a rather wide class of operators, providing a new result even in the unweighted setting…