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Supersymmetry might be broken, in the real world, by anomalies that affect composite operators, while leaving the action supersymmetric. New constraint equations that govern the composite operators and their anomalies are examined. It is…
In Noncommutative Geometry, as in quantum theory, classically real variables are assumed to correspond to self-adjoint operators. We consider the relaxation of the requirement of self-adjointness to mere symmetry for operators $X_i$ which…
The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.
An explicit expression for the Dirichlet-Neumann operator for surface water waves is presented. For non-overturning waves, but without assuming small amplitudes, the formula is first derived in two dimensions, subsequently extrapolated in…
We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous…
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
We prove existence of modified wave operators for one-dimensional Schr\"odinger equations with potential in $L^p(\reals)$, $p<2$. If in addition the potential is conditionally integrable, then the usual M\"oller wave operators exist. We…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…
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…
We describe some classes of linear operators on Banach spaces over non-Archimedean fields, which admit orthogonal spectral decompositions. Several examples are given.
This is a survey on discrete linear operators which, besides approximating in Jackson or near-best order, possess some interpolatory property at some nodes. Such operators can be useful in numerical analysis.
We obtain the partial-wave unitarity constraints on the lowest-dimension effective operators which generate anomalous quartic gauge couplings but leave the triple gauge couplings unaffected. We consider operator expansions with linear and…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…
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…
We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
We provide a probabilistic characterization of criticality, subcriticality, and supercriticality for subordinated Schr\"{o}dinger operators. We also investigate the relationship between the subcriticality of these operators and the uniform…
We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the third order on a two dimensional manifold and show their application to the equivalence problem of such…