SPHERICAL COVARIANCE REPRESENTATIONS

Sergey G. Bobkov; Devraj Duggal

SPHERICAL COVARIANCE REPRESENTATIONS

Sergey G. Bobkov
, Devraj Duggal

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the concentration of measure phenomenon, including second order concen tration inequalities. A detail account is also given in the case of the circle, with a short overview of Höffding's kernels and covariance identities in the class of periodic functions.

Original language	English (US)
Pages (from-to)	239-283
Number of pages	45
Journal	Pure and Applied Functional Analysis
Volume	10
Issue number	2
State	Published - 2025

Bibliographical note

Publisher Copyright:
© 2025, Yokohama Publications. All rights reserved.

Keywords

Covariance representations
Höffding's kernels

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title = "SPHERICAL COVARIANCE REPRESENTATIONS",

abstract = "Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the concentration of measure phenomenon, including second order concen tration inequalities. A detail account is also given in the case of the circle, with a short overview of H{\"o}ffding's kernels and covariance identities in the class of periodic functions.",

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year = "2025",

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AU - Bobkov, Sergey G.

AU - Duggal, Devraj

PY - 2025

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N2 - Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the concentration of measure phenomenon, including second order concen tration inequalities. A detail account is also given in the case of the circle, with a short overview of Höffding's kernels and covariance identities in the class of periodic functions.

AB - Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the concentration of measure phenomenon, including second order concen tration inequalities. A detail account is also given in the case of the circle, with a short overview of Höffding's kernels and covariance identities in the class of periodic functions.

KW - Covariance representations

KW - Höffding's kernels

UR - https://www.scopus.com/pages/publications/105007737134

UR - https://www.scopus.com/pages/publications/105007737134#tab=citedBy

M3 - Article

AN - SCOPUS:105007737134

SN - 2189-3756

VL - 10

SP - 239

EP - 283

JO - Pure and Applied Functional Analysis

JF - Pure and Applied Functional Analysis

IS - 2

ER -

SPHERICAL COVARIANCE REPRESENTATIONS

Abstract

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