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Izv. RAN. Ser. Mat., 1994, Volume 58, Issue 1, Pages 182–194 (Mi izv821)  

This article is cited in 14 scientific papers (total in 14 papers)

New two-radii theorems in the theory of harmonic functions

V. V. Volchkov

Abstract: Functions satisfying the mean value equation over balls of several fixed radii are investigated. A number of substantial amplifications of known theorems of Delsarte and Flatto are obtained. Considered also is the case when the mean value equation is satisfied only approximately (restriction on the growth of the difference between the value of the function at the center of a ball and the mean value over that ball), but nevertheless allows deduction of harmonicity of the function under certain conditions.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:1, 181–192

Bibliographic databases:

UDC: 517.5
MSC: 31B05
Received: 21.07.1992

Citation: V. V. Volchkov, “New two-radii theorems in the theory of harmonic functions”, Izv. RAN. Ser. Mat., 58:1 (1994), 182–194; Russian Acad. Sci. Izv. Math., 44:1 (1995), 181–192

Citation in format AMSBIB
\by V.~V.~Volchkov
\paper New two-radii theorems in the theory of harmonic functions
\jour Izv. RAN. Ser. Mat.
\yr 1994
\vol 58
\issue 1
\pages 182--194
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 44
\issue 1
\pages 181--192

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    This publication is cited in the following articles:
    1. V. V. Volchkov, “The final version of the mean value theorem for harmonic functions”, Math. Notes, 59:3 (1996), 247–252  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. V. Volchkov, “Solution of the support problem for several function classes”, Sb. Math., 188:9 (1997), 1279–1294  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. V. Volchkov, “Uniqueness theorems for some classes of functions with zero spherical means”, Math. Notes, 62:1 (1997), 50–55  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. V. V. Volchkov, “Extremal problems on Pompeiu sets”, Sb. Math., 189:7 (1998), 955–976  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. V. V. Volchkov, “Injectivity sets of the Pompeiu transform”, Sb. Math., 190:11 (1999), 1607–1622  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. V. V. Volchkov, “Injectivity sets for the Radon transform over a sphere”, Izv. Math., 63:3 (1999), 481–493  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Vit. V. Volchkov, “On functions with zero spherical means of complex hyperbolic spaces”, Math. Notes, 68:4 (2000), 436–443  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. V. V. Volchkov, “Extremal problems on Pompeiu sets. II”, Sb. Math., 191:5 (2000), 619–632  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. V. V. Volchkov, “A definitive version of the local two-radii theorem on hyperbolic spaces”, Izv. Math., 65:2 (2001), 207–229  mathnet  crossref  crossref  mathscinet  zmath
    10. V. V. Volchkov, “Theorems on ball mean values in symmetric spaces”, Sb. Math., 192:9 (2001), 1275–1296  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. Vit. V. Volchkov, “Functions with zero ball means on the quaternionic hyperbolic space”, Izv. Math., 66:5 (2002), 875–903  mathnet  crossref  crossref  mathscinet  zmath
    12. Vit. V. Volchkov, “Uniqueness Theorems for Periodic (in Mean) Functions on Quaternion Hyperbolic Space”, Math. Notes, 74:1 (2003), 30–37  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. V. V. Volchkov, “Uniqueness theorems for solutions of the convolution equation on symmetric spaces”, Izv. Math., 70:6 (2006), 1077–1092  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. V. V. Volchkov, “A local two-radii theorem for quasianalytic classes of functions”, Math. Notes, 80:4 (2006), 468–477  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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