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Mat. Sb., 1997, Volume 188, Number 9, Pages 13–30 (Mi msb255)  

This article is cited in 29 scientific papers (total in 29 papers)

Solution of the support problem for several function classes

V. V. Volchkov

Donetsk National University

Abstract: Several classes of functions with zero integrals over all balls of a fixed radius are studied. A description of functions in such classes as series in special functions is obtained and a theorem on a removable singularity is proved. These results make it possible to solve completely the support problem for several classes of functions with zero ball averages. As a consequence, a far-reaching generalization of the well-known Zalcman's two-radii theorem is obtained.


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English version:
Sbornik: Mathematics, 1997, 188:9, 1279–1294

Bibliographic databases:

UDC: 517.5
MSC: 53C65, 44A35
Received: 21.10.1996

Citation: V. V. Volchkov, “Solution of the support problem for several function classes”, Mat. Sb., 188:9 (1997), 13–30; Sb. Math., 188:9 (1997), 1279–1294

Citation in format AMSBIB
\by V.~V.~Volchkov
\paper Solution of the~support problem for several function classes
\jour Mat. Sb.
\yr 1997
\vol 188
\issue 9
\pages 13--30
\jour Sb. Math.
\yr 1997
\vol 188
\issue 9
\pages 1279--1294

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    This publication is cited in the following articles:
    1. V. V. Volchkov, “Injectivity sets of the Pompeiu transform”, Sb. Math., 190:11 (1999), 1607–1622  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Volchkov, VV, “Functions with zero integrals over parallelepipeds”, Doklady Akademii Nauk, 369:4 (1999), 444  mathnet  mathscinet  zmath  isi
    3. V. V. Volchkov, “Extremal problems on Pompeiu sets. II”, Sb. Math., 191:5 (2000), 619–632  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. 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
    5. 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
    6. V. V. Volchkov, “Theorems on ball mean values in symmetric spaces”, Sb. Math., 192:9 (2001), 1275–1296  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Volchkov, VV, “A local two-radius theorem on symmetric spaces”, Doklady Mathematics, 64:3 (2001), 398  mathscinet  zmath  isi
    8. Ochakovskaya, OA, “On functions with zero integrals over balls of fixed radius on the half-space”, Doklady Mathematics, 64:3 (2001), 413  zmath  isi
    9. 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
    10. Volchkov, VV, “Final version of the local two-radius theorem on the quaternion hyperbolic space”, Doklady Mathematics, 65:3 (2002), 389  mathscinet  zmath  isi
    11. Siberian Math. J., 43:2 (2002), 215–222  mathnet  crossref  mathscinet  zmath  isi  scopus
    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, “A local two-radii theorem for quasianalytic classes of functions”, Math. Notes, 80:4 (2006), 468–477  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. 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
    15. V. V. Volchkov, “Local two-radii theorem in symmetric spaces”, Sb. Math., 198:11 (2007), 1553–1577  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. V. V. Volchkov, “On the Injectivity of the Local Pompeiu Transform on the Sphere”, Math. Notes, 81:1 (2007), 51–60  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    17. 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  scopus  scopus  scopus
    18. 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
    19. Ochakovskaya, OA, “MAJORANTS OF FUNCTIONS WITH VANISHING INTEGRALS OVER BALLS”, Ukrainian Mathematical Journal, 60:6 (2008), 1003  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    20. Ochakovskaya, OA, “Majorants of functions with zero integrals over balls of fixed radius”, Doklady Mathematics, 77:3 (2008), 446  crossref  mathscinet  zmath  isi  scopus  scopus
    21. Ochakovskaya O.A., “On the Injectivity of the Pompeiu Transform for Integral Ball Means”, Ukrainian Math J, 63:3 (2011), 416–424  crossref  mathscinet  isi  scopus
    22. V. V. Volchkov, Vit. V. Volchkov, “Spherical means on two-point homogeneous spaces and applications”, Izv. Math., 77:2 (2013), 223–252  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. Ochakovskaya O.A., “Injectivity Classes of the Pompeiu Transformation”, Ukr. Math. J., 64:12 (2013), 1893–1902  crossref  mathscinet  zmath  isi  scopus  scopus
    24. 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
    25. Volchkov V.V., Savost'yanova I.M., “Smoothing of the Singularities of Functions Whose Integrals Over the Balls on a Sphere Are Zero”, Ukr. Math. J., 67:2 (2015), 314–322  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    26. Vit. V. Volchkov, N. P. Volchkova, “The extension problem for functions with zero weighted spherical means”, Russian Math. (Iz. VUZ), 61:8 (2017), 13–21  mathnet  crossref  isi
    27. Vit. V. Volchkov, N. P. Volchkova, “The removability problem for functions with zero spherical means”, Siberian Math. J., 58:3 (2017), 419–426  mathnet  crossref  crossref  isi  elib  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
    29. N. P. Volchkova, Vit. V. Volchkov, “A one-radius theorem on a sphere with pricked point”, Ufa Math. J., 11:4 (2019), 3–12  mathnet  crossref  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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