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

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

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
\Bibitem{Vol94} \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 \mathnet{http://mi.mathnet.ru/izv821} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1271520} \zmath{https://zbmath.org/?q=an:0834.31004} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1995IzMat..44..181V} \transl \jour Russian Acad. Sci. Izv. Math. \yr 1995 \vol 44 \issue 1 \pages 181--192 \crossref{https://doi.org/10.1070/IM1995v044n01ABEH001588} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995QU91700009} 

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