ON the INTEGRAL FORMULAS of CROFTON and HURWITZ RELATIVE to the VISUAL ANGLE of A CONVEX SET

Julià Cufí; Eduardo Gallego; Agustí Reventós

doi:10.1112/S0025579319000202

ON the INTEGRAL FORMULAS of CROFTON and HURWITZ RELATIVE to the VISUAL ANGLE of A CONVEX SET

Julià Cufí, Eduardo Gallego, Agustí Reventós

Department of Mathematics

Research output: Contribution to journal › Article › Research

1 Citation (Scopus)

Abstract

© 2019 University College London. We provide a unified approach that encompasses some integral formulas for functions of the visual angle of a compact convex set due to Crofton, Hurwitz and Masotti. The basic tool is an integral formula that also allows us to integrate new functions of the visual angle. Also, we establish some upper and lower bounds for the considered integrals, generalizing, in particular, those obtained by Santaló for Masotti's integral.

Original language	English
Pages (from-to)	874-896
Journal	Mathematika
Volume	65
DOIs	https://doi.org/10.1112/S0025579319000202
Publication status	Published - 1 Jan 2019

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title = "ON the INTEGRAL FORMULAS of CROFTON and HURWITZ RELATIVE to the VISUAL ANGLE of A CONVEX SET",

abstract = "{\textcopyright} 2019 University College London. We provide a unified approach that encompasses some integral formulas for functions of the visual angle of a compact convex set due to Crofton, Hurwitz and Masotti. The basic tool is an integral formula that also allows us to integrate new functions of the visual angle. Also, we establish some upper and lower bounds for the considered integrals, generalizing, in particular, those obtained by Santal{\'o} for Masotti's integral.",

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AU - Gallego, Eduardo

AU - Reventós, Agustí

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N2 - © 2019 University College London. We provide a unified approach that encompasses some integral formulas for functions of the visual angle of a compact convex set due to Crofton, Hurwitz and Masotti. The basic tool is an integral formula that also allows us to integrate new functions of the visual angle. Also, we establish some upper and lower bounds for the considered integrals, generalizing, in particular, those obtained by Santaló for Masotti's integral.

AB - © 2019 University College London. We provide a unified approach that encompasses some integral formulas for functions of the visual angle of a compact convex set due to Crofton, Hurwitz and Masotti. The basic tool is an integral formula that also allows us to integrate new functions of the visual angle. Also, we establish some upper and lower bounds for the considered integrals, generalizing, in particular, those obtained by Santaló for Masotti's integral.

U2 - 10.1112/S0025579319000202

DO - 10.1112/S0025579319000202

M3 - Article

VL - 65

SP - 874

EP - 896

JO - Mathematika

JF - Mathematika

SN - 0025-5793

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