Related papers: Generalized Double Operator Integrals: Finite Dime…
Density operators are one of the key ingredients of quantum theory. They can be constructed in two ways: via a convex sum of 'doubled kets' (i.e. mixing), and by tracing out part of a 'doubled' two-system ket (i.e. dilation). Both…
Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…
Dynamic multi-objective optimization (DMOO) has recently attracted increasing interest from both academic researchers and engineering practitioners, as numerous real-world applications that evolve over time can be naturally formulated as…
We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest. After…
We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and…
We introduce a generalized index for certain meromorphic, unbounded, operator-valued functions. The class of functions is chosen such that energy parameter dependent Dirichlet-to-Neumann maps associated to uniformly elliptic partial…
While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces, i.e., operators. We study the problem of learning…
We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying…
Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…
Approximation rates are analyzed for deep surrogates of maps between infinite-dimensional function spaces, arising e.g. as data-to-solution maps of linear and nonlinear partial differential equations. Specifically, we study approximation…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…
This thesis proposes a combinatorial generalization of a nilpotent operator on a vector space. The resulting object is highly natural, with basic connections to a variety of fields in pure mathematics, engineering, and the sciences. For the…
Density operators are one of the key ingredients of quantum theory. They can be constructed in two ways: via a convex sum of `doubled kets' (i.e. mixing), and by tracing out part of a `doubled' two-system ket (i.e. dilation). Both…
This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…
We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…
Doubly occupied configuration interaction (DOCI) with optimized orbitals often accurately describes strong correlations while working in a Hilbert space much smaller than that needed for full configuration interaction. However, the scaling…
In this work, a class of semiclassical Fourier Integral Operators (FIOs) with complex phase associated to some canonical transformation of the phase space $T^*\R^d$ is constructed. Upon some general boundedness assumptions on the symbol and…
A theorem that is of aid in computing the domain of the adjoint operator is provided. It may serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally normal operator or for $H$--selfadjointness of…
We establish a formal connection between the problem of characterizing degrees of freedom (DoF) in constant single-antenna interference channels (ICs), with general channel matrix, and the field of additive combinatorics. The theory we…