@inbook{10.2307/j.ctt130hk7z.5,
URL = {http://www.jstor.org/stable/j.ctt130hk7z.5},
abstract = {Chapter I may be thought of as a review of some known facts which are basic in motivating our theory. Proofs are for the most part only sketched.Denote x = (x1, …, xn). Fix positive exponebts a1, …, an, and define${{\delta }_{\text{t}}}(\text{x})=({{\text{t}}^{{{\text{a}}_{1}}}}{{\text{x}}_{1}},\ldots ,{{\text {t}}^{{{\text{a}}_{\text{n}}}}}{{\text{x}}_{\text{n}}}), 0 < t < \infty $. Observe that(1) δs∘ δst(2) δ1= Id(3) δt(x) → 0 as t → 0 for all x(More generally, one might let δtbe given by multiplication by the matrix eAlogtwhere A is a real matrix whose eigenvalues all have positive real part.)The change of variable formula for dilations δt},
bookauthor = {ALEXANDER NAGEL and ΕLIAS M. STEIN},
booktitle = {Lectures on Pseudo-Differential Operators: Regularity Theorems and Applications to Non-Elliptic Problems. (MN-24)},
pages = {7--30},
publisher = {Princeton University Press},
title = {Homogeneous distributions},
year = {1979}
}