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Mat. Sb., 1995, Volume 186, Number 6, Pages 15–34 (Mi msb43)  

This article is cited in 28 scientific papers (total in 28 papers)

A definitive version of the local two-radii theorem

V. V. Volchkov

Donetsk National University

Abstract: Various classes of functions with zero integrals over all balls of a fixed radius are studied. For functions in such classes a description in the form of a series in special functions is obtained and a uniqueness theorem is proved. These results make it possible to solve completely the problem of existence of a non-trivial function with zero integrals over all balls of radius assuming either of two given values.

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English version:
Sbornik: Mathematics, 1995, 186:6, 783–802

Bibliographic databases:

UDC: 517.5
MSC: 53C65, 44A35
Received: 24.08.1994

Citation: V. V. Volchkov, “A definitive version of the local two-radii theorem”, Mat. Sb., 186:6 (1995), 15–34; Sb. Math., 186:6 (1995), 783–802

Citation in format AMSBIB
\by V.~V.~Volchkov
\paper A definitive version of the~local two-radii theorem
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 6
\pages 15--34
\jour Sb. Math.
\yr 1995
\vol 186
\issue 6
\pages 783--802

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    This publication is cited in the following articles:
    1. 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
    2. V. V. Volchkov, “Extremal problems on Pompeiu sets”, Sb. Math., 189:7 (1998), 955–976  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. 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
    4. Volchkov, VV, “Functions with zero integrals over parallelepipeds”, Doklady Akademii Nauk, 369:4 (1999), 444  mathnet  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. 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
    7. V. V. Volchkov, “Extremal problems on Pompeiu sets. II”, Sb. Math., 191:5 (2000), 619–632  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. V. V. Volchkov, “Theorems on ball mean values in symmetric spaces”, Sb. Math., 192:9 (2001), 1275–1296  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. Volchkov, VV, “A local two-radius theorem on symmetric spaces”, Doklady Mathematics, 64:3 (2001), 398  mathscinet  zmath  isi
    10. Ochakovskaya, OA, “On functions with zero integrals over balls of fixed radius on the half-space”, Doklady Mathematics, 64:3 (2001), 413  mathscinet  zmath  isi
    11. Volchkov, VV, “Inversion of the local Pompeiu transform on the quaternion hyperbolic space”, Doklady Mathematics, 64:1 (2001), 90  mathscinet  zmath  isi
    12. 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
    13. 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
    14. Volchkov, VV, “Final version of the local two-radius theorem on the quaternion hyperbolic space”, Doklady Mathematics, 65:3 (2002), 389  mathscinet  zmath  isi
    15. Volchkov, VV, “On mean periodic functions on complex hyperbolic spaces”, Siberian Mathematical Journal, 43:2 (2002), 215  mathnet  crossref  mathscinet  zmath  isi  elib
    16. 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
    17. Vit. V. Volchkov, N. P. Volchkova, “Inversion theorems for the Pompeiu local transformation on the quaternion hyperbolic space”, St. Petersburg Math. J., 15:5 (2003), 753–771  mathnet  crossref  mathscinet  zmath
    18. Volchkov V., “Theorems on the Injectivity of the Local Pompeiu Transform on the Sphere”, Dokl. Math., 68:3 (2003), 363–365  mathnet  mathscinet  isi
    19. 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
    20. 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
    21. Ochakovskaya, OA, “Liouville-type theorems for functions with zero integrals over balls of fixed radius”, Doklady Mathematics, 76:1 (2007), 530  crossref  mathscinet  zmath  isi
    22. V. V. Volchkov, “Local two-radii theorem in symmetric spaces”, Sb. Math., 198:11 (2007), 1553–1577  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    23. Ochakovskaya, OA, “MAJORANTS OF FUNCTIONS WITH VANISHING INTEGRALS OVER BALLS”, Ukrainian Mathematical Journal, 60:6 (2008), 1003  crossref  mathscinet  zmath  isi
    24. O. A. Ochakovskaya, “Precise characterizations of admissible rate of decrease of a non-trivial function with zero ball means”, Sb. Math., 199:1 (2008), 45–65  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    25. Ochakovskaya O.A., “Analogues of the Problem of Analytic Continuation From Circles for Some Differential Equations”, Dokl. Math., 82:1 (2010), 581–582  crossref  mathscinet  zmath  isi
    26. 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
    27. V. V. Volchkov, Vit. V. Volchkov, “Local two-radii theorems on the multi-dimensional sphere”, Izv. Math., 78:1 (2014), 1–21  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    28. Vit. V. Volchkov, N. P. Volchkova, “Vektornye polya s nulevym potokom cherez sfery fiksirovannogo radiusa”, Vladikavk. matem. zhurn., 20:4 (2018), 20–34  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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