Affiliation:
1. Institute of Mathematics Yerevan Armenia
2. Southern Federal University Rostov‐on‐Don Russia
Abstract
We consider the problem of restoring a two‐dimensional convex source of gravity based on values of its potential function on a union of half‐planes. With that aim we prove a Paley–Wiener type theorem for functions of exponential type in a sector. In particular, we find the maximal set of analytic continuation whose complement is convex inside a sector. Our result serves as a sectorial analog of G. Polya's indicator theorem. It corrects, simplifies, and extends a result of M. Morimoto. It also improves a related result of M. Dzhrbashyan and A. Avetisyan.
Funder
Southern Federal University
Subject
General Engineering,General Mathematics
Cited by
1 articles.
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