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Mat. Zametki, 2015, Volume 97, Issue 3, Pages 397–406 (Mi mz10599)  

This article is cited in 2 scientific papers (total in 2 papers)

Sets of Uniqueness for Harmonic and Analytic Functions and Inverse Problems for Wave Equations

M. Yu. Kokurin

Mari State University, Ioshkar-Ola

Abstract: Several examples of one-dimensional analytic sets of uniqueness for harmonic functions on the sphere in $\mathbb{R}^3$ are given and some examples of analytic sets on the sphere in $\mathbb{R}^n$ which cannot contain sets of uniqueness are presented. Analytic curves which are sets of uniqueness for real-analytic functions in $\mathbb{R}^n$, $n \ge 3$, are constructed. The obtained results are used to justify the inhomogeneity sounding schemes when the inverse problem of acoustic scattering is solved under the conditions that the source and detector coordinates coincide.

Keywords: inhomogeneity sounding, set of uniqueness, inverse scattering problem, acoustic sounding scheme.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00239a
This work was supported by the Russian Foundation for Basic Research (grant no. 12-01-00239a).


DOI: https://doi.org/10.4213/mzm10599

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English version:
Mathematical Notes, 2015, 97:3, 376–383

Bibliographic databases:

Document Type: Article
UDC: 517.57+517.518.25+519.642.3
Received: 22.02.2014
Revised: 28.10.2014

Citation: M. Yu. Kokurin, “Sets of Uniqueness for Harmonic and Analytic Functions and Inverse Problems for Wave Equations”, Mat. Zametki, 97:3 (2015), 397–406; Math. Notes, 97:3 (2015), 376–383

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Arendt W., “Vector-valued holomorphic and harmonic functions”, Concr. Operators, 3:1 (2016), 68–76  crossref  mathscinet  zmath  isi
    2. M. Yu. Kokurin, “On the Completeness of Products of Harmonic Functions and the Uniqueness of the Solution of the Inverse Acoustic Sounding Problem”, Math. Notes, 104:5 (2018), 689–695  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
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