来自群轨道的复杂球形设计

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2024-04-27 DOI:10.1016/j.jat.2024.106047

Mozhgan Mohammadpour, Shayne Waldron

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引用次数: 0

摘要

我们考虑的一般问题是，在有限群的单元作用下，什么时候所有轨道都是复球面设计。那些具有大稳定器的轨道是最佳复球面设计的良好候选者。为此，我们发展了复杂设计的一般理论和群作用的相关（谐波）莫连级数。作为应用，我们给出了一些推定最优实球面和复球面 t 设计的明确构造。

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Complex spherical designs from group orbits

We consider the general question of when all orbits under the unitary action of a finite group give a complex spherical design. Those orbits which have large stabilisers are then good candidates for being optimal complex spherical designs. This is done by developing the general theory of complex designs and associated (harmonic) Molien series for group actions. As an application, we give explicit constructions of some putatively optimal real and complex spherical $t$ -designs.

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.