On some identities involving spherical means

Cimmino, Gianfranco. "On some identities involving spherical means." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 83.1 (1989): 69-72. <http://eudml.org/doc/287439>.

@article{Cimmino1989,
abstract = {For every positive definite quadratic form in $n$ variables the reciprocal of the square root of the discriminant is equal to the arithmetic mean of the values assumed by the form on the $n-1$ sphere centered at $0$ and with radius $1$ raised to the ($-\frac\{n\}\{2\}$)-th. power. Various consequences are deduced from this, in particular a simplification of some calculations from which one obtains the possibility of solving linear systems using spherical means rather than determinants.},
author = {Cimmino, Gianfranco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Spherical means; Quadratic forms; Linear systems; positive definite quadratic form; discriminant; arithmetic mean; linear systems; spherical means},
language = {eng},
month = {12},
number = {1},
pages = {69-72},
publisher = {Accademia Nazionale dei Lincei},
title = {On some identities involving spherical means},
url = {http://eudml.org/doc/287439},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Cimmino, Gianfranco
TI - On some identities involving spherical means
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 69
EP - 72
AB - For every positive definite quadratic form in $n$ variables the reciprocal of the square root of the discriminant is equal to the arithmetic mean of the values assumed by the form on the $n-1$ sphere centered at $0$ and with radius $1$ raised to the ($-\frac{n}{2}$)-th. power. Various consequences are deduced from this, in particular a simplification of some calculations from which one obtains the possibility of solving linear systems using spherical means rather than determinants.
LA - eng
KW - Spherical means; Quadratic forms; Linear systems; positive definite quadratic form; discriminant; arithmetic mean; linear systems; spherical means
UR - http://eudml.org/doc/287439
ER -