Related papers: Multiple singular values of Hankel operators

In this note, we shall prove a formula for the Fourier transform of spherical Bessel functions over complex numbers, viewed as the complex analogue of the classical formulae of Hardy and Weber. The formula has strong representation…

In this paper a twofold inverse problem for orthogonal matrix functions in the Wiener class is considered. The scalar-valued version of this problem was solved by Ellis and Gohberg in 1992. Under reasonable conditions, the problem is…

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…

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…

Throughout the 1980's, Kudla and the second named author studied integral transforms from rapidly decreasing closed differential forms on arithmetic quotients of the symmetric spaces of orthogonal and unitary groups to spaces of classical…

For $G=\mathrm{SL}_2$ or $\mathrm{GL}_2$, we present explicit formulas for the nonabelian Fourier kernels on $G$, as conjectured by A. Braverman and D. Kazhdan. Additionally, we furnish explicit formulas for the orbital Hankel transform on…

A proof is given for the Fourier transform for functions in a quantum mechanical Hilbert space on a non-compact manifold in general relativity. In the (configuration space) Newton-Wigner representation we discuss the spectral decomposition…

Given two arbitrary sequences $(\lambda_j)_{j\ge 1}$ and $(\mu_j)_{j\ge 1}$ of real numbers satisfying $$|\lambda_1|>|\mu_1|>|\lambda_2|>|\mu_2|>...>| \lambda_j| >| \mu_j| \to 0\ ,$$ we prove that there exists a unique sequence…

We prove multiplicity one for vector valued holomorphic Siegel modular forms of weights greater or equal to 3 and the full Siegel modular group and give a trace formula for the action of the Hecke operators T(p) in the regular cases.

Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be…

We present a numerical method for the solution of linear magnetostatic problems in domains with a symmetry direction, including axial and translational symmetry. The approach uses a Fourier series decomposition of the vector potential…

Let V be a finite dimensional vector space over the field with two elements with a given nondegenerate symplectic form. Let [V] be the vector space of complex valued functions on V and let [V]_Z be the subgroup of [V] consisting of integer…

We describe a fast algorithm for computing discrete Hankel transforms of moderate orders from $n$ nonuniform points to $m$ nonuniform frequencies in $O((m+n)\log\min(n,m))$ operations. Our approach combines local and asymptotic Bessel…

We study spectral properties of the Carleman operator (the Hankel operator with kernel $h_{0}(t)=t^{-1}$) and, in particular, find an explicit formula for its resolvent. Then we consider perturbations of the Carleman operator $H_{0}$ by…

Given a CR manifold with non-degenerate Levi form, we show that the operators of the functional calculus for Toeplitz operators are complex Fourier integral operators of Szeg\H{o} type. As an application, we establish semi-classical…

We consider compact Hankel operators realized in $\ell^2(\mathbb Z_+)$ as infinite matrices $\Gamma$ with matrix elements $h(j+k)$. Roughly speaking, we show that, for all $\alpha>0$, the singular values $s_{n}$ of $\Gamma$ satisfy the…

In this paper we characterize compact Hankel operators with conjugate holomorphic symbols on the Bergman space of bounded convex Reinhardt domains in $\mathbb{C}^2$. We also characterize compactness of Hankel operators with conjugate…

We introduce a trilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue. We demonstrate that for a canonical spectral triple over a closed spin manifold it recovers the…

We consider $\mathbb{R}^3$ as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary $\tau\in \widehat{SO(3)}$, let $E_\tau$ be the homogeneous vector bundle over $\mathbb{R}^3$…

A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence…