Inverse scattering problems and restoration of a function from the modulus of its Fourier transform
type: Item
instance of: scholarly article
title: Inverse scattering problems and restoration of a function from the modulus of its Fourier transform
zbMATH Open document ID: 0655.35077
DOI: 10.1007/BF00969199
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The author solves the following inverse problem: given a bounded domain \(\Omega\) in \({\mathbb{R}}^ n\), recover the function \(f\in C({\bar \Omega})\) from the knowledge of \[ g(x)=| \int_{\Omega}e^{-i<x,\xi >}f(\xi)d\xi |^ 2\quad (x\in {\mathbb{R}}^ n). \] Uniqueness theorems (up to ``rotations'') are proved, generalizing previous work by H. A. Ferweda, B. J. Hoenders, A. M. J. Huiser, and E. Wolf. The results have been announced earlier in Dokl. Akad. Nauk SSSR 279, No.6, 1348-1351 (1984).
reviewed by: Jürgen Appell
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 42B10
zbMATH DE Number: 4069466
zbMATH Keywords: inverse problem
zbMATH Keywords: bounded domain
zbMATH Keywords: Uniqueness
Wikidata QID: Q29035928
author: Michael V. Klibanov
MaRDI profile type: Publication
cites work: High frequency asymptotics for the scattering matrix and the inverse problem of acoustical scattering
cites work: Q3994910
cites work: AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
cites work: Q4726811
description: scientific article; zbMATH DE number 4069466