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Mat. Sb., 2008, Volume 199, Number 1, Pages 47–66 (Mi msb3783)  

This article is cited in 8 scientific papers (total in 8 papers)

Precise characterizations of admissible rate of decrease of a non-trivial function with zero ball means

O. A. Ochakovskaya

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

Abstract: Precise characterizations of an admissible rate of decrease of a non-trivial function having zero integrals over all balls of fixed radius are established. The case of an essentially anisotropic behaviour of the function at infinity is considered for the first time. In particular, the function is even allowed to grow exponentially in one variable, which is compensated in a certain sense by its rapid decrease in other variables.
Bibliography: 17 titles.

DOI: https://doi.org/10.4213/sm3783

Full text: PDF file (611 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:1, 45–65

Bibliographic databases:

UDC: 517.444
MSC: Primary 26B15, 43A85; Secondary 53C65
Received: 19.10.2006 and 12.07.2007

Citation: O. A. Ochakovskaya, “Precise characterizations of admissible rate of decrease of a non-trivial function with zero ball means”, Mat. Sb., 199:1 (2008), 47–66; Sb. Math., 199:1 (2008), 45–65

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm3783
  • http://mi.mathnet.ru/eng/msb/v199/i1/p47

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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. Ochakovskaya O.A., “On the injectivity of the Pompeiu transform for integral ball means”, Ukr. Math. J., 63:3 (2011), 416–424  crossref  mathscinet  zmath  isi  scopus
    2. Volchkov V.V., Volchkov Vit.V., “Analogues of the Liouville theorem for solutions of the twisted convolution equation”, Dokl. Math., 83:2 (2011), 197–200  crossref  mathscinet  zmath  isi  elib  scopus
    3. Ochakovskaya O.A., “The boundary behavior of functions with vanishing integrals over hyperbolic disks”, Dokl. Math., 86:1 (2012), 534–536  crossref  mathscinet  zmath  isi  elib  scopus
    4. O. A. Ochakovskaya, “Theorems on ball mean values for solutions of the Helmholtz equation on unbounded domains”, Izv. Math., 76:2 (2012), 365–374  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. V. V. Volchkov, Vit. V. Volchkov, “Behaviour at infinity of solutions of twisted convolution equations”, Izv. Math., 76:1 (2012), 79–93  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Ochakovskaya O.A., “Injectivity classes of the Pompeiu transformation”, Ukr. Math. J., 64:12 (2013), 1893–1902  crossref  mathscinet  zmath  isi  scopus
    7. O. A. Ochakovskaya, “Boundary uniqueness theorems for functions whose integrals over hyperbolic discs vanish”, Sb. Math., 204:2 (2013), 264–279  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. O. A. Ochakovskaya, “Radial majorants of functions with zero integrals over balls of a fixed radius”, Izv. Math., 78:3 (2014), 580–595  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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