Related papers: Harmonic Analysis and Localization Technique

We develop a quantum harmonic analysis framework for the affine group. This encapsulates several examples in the literature such as affine localization operators, covariant integral quantizations, and affine quadratic time-frequency…

We establish some results in local harmonic analysis which are necessary for Arthur's invariant trace formula for coverings of connected reductive groups. More precisely, for local coverings we will study (1) the Plancherel formula and its…

We develop a categorical and algebro-geometric treatment of localization for cohomological theories endowed with an open--closed recollement. Starting from a class on a space whose restriction to the open complement vanishes, we show that…

In this paper, we present an overview of the development of one of the most dynamic areas of mathematics today: local differential operators of non-integer order. The underlying question is whether we are witnessing a period of…

The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…

In this paper we introduce and study the algebraic generalization of non commutative convolutional neural networks. We leverage the theory of algebraic signal processing to model convolutional non commutative architectures, and we derive…

Several sets of quaternionic functions are described and studied with respect to hyperholomorphy, addition and (non commutative) multiplication, on open sets of $\mathbb H$. The aim is to get a local function theory.

This paper outlines a covariant theory of operators defined on groups and homogeneous spaces. A systematic use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is…

We consider the concept of a local set of inference rules. A local rule set can be automatically transformed into a rule set for which bottom-up evaluation terminates in polynomial time. The local-rule-set transformation gives…

We aim addition theorems for multivariate Krawtchouk polynomials, following Dunkl(1976) for 1-variate case. We work on harmonic analysis on a non-Archimedean local field, that is a group theoretic situation where these polynomials play…

This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary first step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative…

The notion of Fourier transform is among the more important tools in analysis, which has been generalized in abstract harmonic analysis to the level of abelian locally compact groups. The aim of this paper is to further generalize the…

We introduce the concept of locally homogeneous space, and prove in this context L^p and Holder estimates for singular and fractional integrals, as well as L^p estimates on the commutator of a singular or fractional integral with a BMO or…

On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg…

Entanglement, as studied in quantum information science, and non-local quantum correlations, as studied in condensed matter physics, are fundamentally akin to each other. However, their relationship is often hard to quantify due to the lack…

In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…

Quantum harmonic analysis extends classical harmonic analysis by integrating quantum mechanical observables, replacing functions with operators and classical convolution structures with their noncommutative counterparts. This paper explores…

The article explores function terms within uniform theories. It examines the uniformity of these theories through an algebraic lens. The paper compares the uniformity of terms and predicates within axiom schemas. It demonstrates the…

Following the idea of the fractional space-time Fourier transform, a linear canonical space-time transform for 16-dimensional space-time $C\ell_{3,1}$-valued signals is investigated in this paper. First, the definition of the proposed…

Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for non-local field theories in d space-time dimensions by considering auxiliary d+1 dimensional field theories which are local with respect to…