Тип публикации: статья из журнала
Год издания: 2021
Идентификатор DOI: 10.1070/SM9328
Ключевые слова: weierstrass's preparation theorem, analytic set, regular point, volume of an analytic set, wirtinger's theorem, weierstrass’s preparation theorem, wirtinger’s theorem.
Аннотация: Given a holomorphic function f(sigma, z), sigma is an element of C-m, z is an element of C-n, an estimate for the volume of the zero set {z : f(sigma, z) = 0} is presented which holds uniformly in sigma. Such estimates are quite useful in investigations of oscillatory integrals of the form J(lambda, sigma) = integral(n alpha(sigma,Показать полностью)(R) x)(ei lambda Phi(sigma,x)) dc as sigma -> infinity. Here a(sigma, x) is an element of C-0(infinity) (R-n x R-m) is a so-called amplitude function and F(s, x) is a phase function. Bibliography: 9 titles. Given a holomorphic function , , , an estimate for the volume of the zero set is presented which holds uniformly in . Such estimates are quite useful in investigations of oscillatory integrals of the form as . Here is a so-called amplitude function and is a phase function. Bibliography: 9 titles. © 2021 Russian Academy of Sciences (DoM) and London Mathematical Society.
Журнал: SBORNIK MATHEMATICS
Выпуск журнала: Vol. 212, Is. 11
Номера страниц: 1608-1614
ISSN журнала: 10645616
Место издания: BRISTOL
Издатель: TURPION LTD