Related papers: Time-frequency Analysis of Born-Jordan Pseudodiffe…
We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of…
A criterion for subnormality of unbounded composition operators in L2-spaces, written in terms of measurable families of probability measures satisfying the so-called consistency condition, is established. It becomes a new characterization…
A long standing problem of Gian-Carlo Rota for associative algebras is the classification of all linear operators that can be defined on them. In the 1970s, there were only a few known operators, for example, the derivative operator, the…
We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the wave front map becomes a functor into the…
Gradients of neural networks can be computed efficiently for any architecture, but some applications require differential operators with higher time complexity. We describe a family of restricted neural network architectures that allow…
This article explores an algebraic-recursive approach to construct differential operators that commute with a central operator $\hat{H}$ in quantum mechanics. Starting from the Schr\"odinger equation for a free particle, the work derives…
We give a complete description of order isomorphisms between operator intervals in general von Neumann algebras. For the description, we use Jordan $^*$-isomorphisms and locally measurable operators. Our results generalize several works by…
We classify the possible Jordan canonical forms of self-adjoint operators in Minkowski space-time (in fact in pseudo-Euclidean space, i.e. an indefinite inner product space) and we show how to obtain a Jordan canonical basis which also puts…
Details of the contents and the formulations of the Born rule changed considerably from its inception by Born in 1926 to the present day. This paper traces the early history of the Born rule 100 years ago, its generalization (essential for…
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and…
This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type $1,1$ in H\"ormander's sense. Thus, it contributes to the long-standing problem of…
In this paper the p -adic Lizorkin spaces of test functions and distributions are introduced, and multidimensional Vladimirov's and Taibleson's fractional operators are studied on these spaces. Since the p -adic Lizorkin spaces are…
In this paper we revisit the hypothesis needed to define the "paracomposition" operator, an analogue to the classic pull-back operation in the low regularity setting, first introduced by S. Alinhac in [3]. More precisely we do so in two…
In this paper, we introduce the Rogers-Szeg\"o deformed $q$-differential operators g$_{n}(bD_{q}|u)$ based on $q$-differential operator $D_{q}$. The motivation for introducing the operators g$_{n}(bD_{q})$ is that their limit turns out to…
In this work, we extend Wigner's original framework to analyze linear operators by examining the relationship between their Wigner and Schwartz kernels. Our approach includes the introduction of (quasi-)algebras of Fourier integral…
The Born-Jordan method for constructing the quantum condition of the Matrix Mechanics is pointed out to be inappropriate in the present work. We modify this method and reconstruct the quantum condition by setting up a new expression for the…
We will present versions of the Rellich-Kondrachov theorem for pseudo-differential operators acting on localizable Hardy spaces. One of the techniques includes boundedness properties for pseudodifferential operators with symbols in the…
I review the concept of a {\em disorder operator}, introduced originally by Kadanoff in the context of the two-dimensional Ising model. Disorder operators acquire an expectation value in the disordered phase of the classical spin system.…
We study the boundedness of rough Fourier integral and pseudodifferential operators, defined by general rough H\"ormander class amplitudes, on Banach and quasi-Banach $L^p$ spaces. Thereafter we apply the aforementioned boundedness in order…
We introduce a new formalism of differential operators for a general associative algebra A. It replaces Grothendieck's notion of differential operator on a commutative algebra in such a way that derivations of the commutative algebra are…