Related papers: Harmonic Analysis over adelic spaces
We employ functional analysis techniques in order to deduce that some classical and recent interpolation results in Fourier analysis can be suitably perturbed. As an application of our techniques, we obtain generalizations of Kadec's…
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing…
In this paper we generalize and put in a new light part of ``Fouier analysis on Number fields and Hecke's zeta function''[14] by Tate. We express the relative Euler characteristic using purely adelic language. By using certain natural…
Let $V_1,V_2,V_3$ be a triple of even dimensional vector spaces over a number field $F$ equipped with nondegenerate quadratic forms $\mathcal{Q}_1,\mathcal{Q}_2,\mathcal{Q}_3$, respectively. Let $Y \subset \prod_{i=1}^3 V_i$ be the closed…
We prove various results connecting structural or algebraic properties of graphs and groups to conditions on their spaces of harmonic functions. In particular: we show that a group with a finitely supported symmetric measure has a…
We present a simple representation for analytically continued nested harmonic sums for the arbitrary complex argument. This representation can be obtained for a wide range of nested harmonic sums from a precomputed database for the pole…
This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so…
Using a Poisson bracket representation, in 3D, of the Lie algebra $\mathfrak{sl}(2)$, we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras…
We develop the quantum harmonic analysis framework in the reducible setting and apply our findings to polyanalytic Fock spaces. In particular, we explain some phenomena observed in arXiv:2201.10230 and answer a few related open questions.…
We sketch recent applications of the harmonic superspace approach for off-shell formulations of $(4,4)$, $2D$ sigma models with torsion and for constructing super KdV hierarchies associated with "small" and "large" $N=4$ superconformal…
Quaternion, an extension of complex number, is the first discovered non-commutative division algebra by William Rowan Hamilton in 1843. In this article, we review the recent progress on building up the connection between the mathematical…
In Vasiliev's unfolded formulation of higher-spin dynamics the standard fields are embedded on-shell into covariantly constant master fields valued in Lorentz-covariant slices of the star-product algebra A of functions on the singleton…
In this paper we extend to finite-dimensional Pontryagin spaces the methods used in \cite{CasazzaLeon,Deguang} to build frames from an adjoint and positive operator. It is proved that any frame in finite dimensional Pontryagin space…
We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using harmonic means and completely partitioned weighted geometric means. Our result…
A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic continuation…
The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.
Using recent results on string on $AdS_{3}\times N^d$, where N is a d-dimensional compact manifold, we re-examine the derivation of the non trivial extension of the (1+2) dimensional-Poincar\'e algebra obtained by Rausch de Traubenberg and…
Polar duality is a fundamental geometric concept that can be interpreted as a form of Fourier transform between convex sets. Meanwhile, the Donoho-Stark uncertainty principle in harmonic analysis provides a framework for comparing the…
Fourier analysis on the Boolean hypercube is fundamentally defined as the orthogonal decomposition of the space of pseudo-Boolean functions with respect to the uniform probability measure. In this work, we propose an ANOVA-based…
In every dimension $d \geq 2$, we give an explicit formula that expresses the values of any Schwartz function on $\mathbb{R}^d$ only in terms of its restrictions, and the restrictions of its Fourier transform, to all origin-centered spheres…