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We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…

Information Theory · Computer Science 2020-11-23 Hugues Randriambololona

As for any symmetric space the tangent space to Siegel upper-half space is endowed with an operation coming from the Lie bracket on the Lie algebra. We consider the pull-back of this operation to the moduli space of curves via the Torelli…

Algebraic Geometry · Mathematics 2021-02-10 Alessandro Ghigi , Carolina Tamborini

We characterize the reproducing kernel Hilbert spaces whose elements are $p$-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for $p=2$ we show that the spectral…

Functional Analysis · Mathematics 2007-05-23 Claudio Carmeli , Ernesto De Vito , Alessandro Toigo

Structured kernel interpolation (SKI) accelerates Gaussian process (GP) inference by interpolating the kernel covariance function using a dense grid of inducing points, whose corresponding kernel matrix is highly structured and thus…

Machine Learning · Computer Science 2023-05-26 Mohit Yadav , Daniel Sheldon , Cameron Musco

In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as kernel functions. This investigation begins with the properties of functions in this space, and here a connection to the classical Hardy…

Functional Analysis · Mathematics 2015-03-06 Joel A. Rosenfeld

We give characterizations of radial Fourier multipliers as acting on radial L^p-functions, 1<p<2d/(d+1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding…

Classical Analysis and ODEs · Mathematics 2010-03-15 Gustavo Garrigos , Andreas Seeger

We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove that such discrete operators extend to bounded operators from $\ell^p$ to $\ell^q$…

Classical Analysis and ODEs · Mathematics 2019-12-19 Lillian B. Pierce

In this paper we study hermitian kernels invariant under the action of a semigroup with involution. We characterize those hermitian kernels which realize the given action by bounded operators on a Krein space. Applications to the GNS…

Functional Analysis · Mathematics 2009-10-31 Tiberiu Constantinescu , Aurelian Gheondea

We examine how the square-integrable function subspaces are transformed using the holomorphic Fourier transform. On account of this, the extended Paley-Wiener theorem over the Hardy-Sobolev spaces is produced. The theorem also asserts that…

Functional Analysis · Mathematics 2024-03-19 Detian Liu , Haichou Li , Kit Ian Kou

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are…

Statistics Theory · Mathematics 2013-08-20 M. Arashi

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Sun and…

Information Theory · Computer Science 2007-07-13 Jonghoon Ryu , Oscar Y. Takeshita

Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the…

Classical Analysis and ODEs · Mathematics 2016-03-24 R. J. Cintra , H. M. de Oliveira

Paragrassmann algebras are given a sesquilinear form for which one subalgebra becomes a Hilbert space known as the Segal-Bargmann space. This Hilbert space as well as the ambient space of the paragrassmann algebra itself are shown to have…

Mathematical Physics · Physics 2012-05-22 Stephen Bruce Sontz

Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…

Computational Geometry · Computer Science 2019-03-07 Stéphane Breuils , Vincent Nozick , Laurent Fuchs , Akihiro Sugimoto

The aim of this paper is to construct sup-exponentially localized kernels and frames in the context of classical orthogonal expansions, namely, expansions in Jacobi polynomials, spherical harmonics, orthogonal polynomials on the ball and…

Classical Analysis and ODEs · Mathematics 2008-09-22 Kamen Ivanov , Pencho Petrushev , Yuan Xu

This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given one as a subspace.…

Machine Learning · Computer Science 2011-02-08 Yuesheng Xu , Haizhang Zhang , Qinghui Zhang

We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…

Machine Learning · Computer Science 2024-01-24 Alvaro Almeida Gomez , Antonio Silva Neto , Jorge zubelli

While direct statements for kernel based interpolation on regions $\Omega \subset \mathbb{R}^d$ are well researched, far less is known about corresponding inverse statements. The available inverse statements for kernel based interpolation…

Numerical Analysis · Mathematics 2025-04-23 Tizian Wenzel

The Weil representation of a real symplectic group $Sp(2n,R)$ admits a canonical extension to a holomorphic representation of a certain complex semigroup consisting of Lagrangian linear relations (this semigroup includes the Olshanski…

Classical Analysis and ODEs · Mathematics 2012-11-28 Tatiana Foth , Yurii A. Neretin

We use weakly holomorphic modular forms for the Hecke theta group to construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the…

Number Theory · Mathematics 2020-02-17 Danylo Radchenko , Maryna Viazovska