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Volchkov, Valerii Vladimirovich

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Total publications: 39
Scientific articles: 39

Number of views:
This page:2750
Abstract pages:11027
Full texts:2983
References:1229
Professor
Doctor of physico-mathematical sciences (1997)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
E-mail:
Keywords: theory of numbers, integral geometry, harmonic analysis, convolutional equations, mean periodicity, the problem of continuation, the Fourier transform, Heisenberg group, twisted convolution equation, two-radii theorems, confluent hypergeometric functions.

Subject:

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. There results make it possible to solve completely the problem of existence of a non-trivial function with zero integrals over balls of radius assuming either of two given values. Also there results make it possible to solve completely the support problem for several classes of functions with zero ball averages. As consequence, a far-reaching generalization of the well-known Zalcman's two-radii theorem is obtained. A solution of the local Pompeiu problem is obtained for functions with vanishing integrals over parallelepipeds lying in a fixed ball. A solution of the problem of describing the kernel of the Radon transform over a sphere with respect to sets with spherical symmetry is obtained. The solution enabled us, in particular, to characterize all injectivity sets of this type. The technique used in the proofs enabled us to obtain other exact results concerning spherical means, namely, new two-radii theorems and a uniqueness theorem.

Biography

Graduated from Mathematical Faculty of Donetsk State University in 1965 (department of mathematical analysis and theory of functions). Ph. D. thesis was defended in 1991. D. Sci. thesis was defended in 1997. A list of my works contains more than 60 titles.

In 1975 I was awarded the prize of the European Academy.

   
Main publications:
  1. Volchkov V. V., “Okonchatelnyi variant lokalnoi teoremy o dvukh radiusakh”, Matem. sb., 186:6 (1995), 15–34  mathnet  mathscinet  zmath
  2. Volchkov V. V., “Reshenie problemy nositelya dlya nekotorykh klassov funktsii”, Matem. sb., 188:9 (1997), 13–30  mathnet  mathscinet  zmath
  3. Volchkov V. V., “O mnozhestvakh in'ektivnosti preobrazovaniya Radona na sferakh”, Izv. RAN, ser. matem., 63:3 (1999), 63–76  mathnet  mathscinet  zmath
  4. Volchkov V. V., “Ekstremalnye zadachi o mnozhestvakh Pompeiyu. II”, Matem. sb., 191:5 (2000), 3–16  mathnet  mathscinet  zmath
  5. Volchkov V. V., “O mnozhestvakh in'ektivnosti preobrazovaniya Pompeiyu”, Matem. sb., 190:11 (1999), 51–66  mathnet  mathscinet  zmath

http://www.mathnet.ru/eng/person8322
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/683831

Publications in Math-Net.Ru
2018
1. V. V. Volchkov, Vit.†V.†Volchkov, “Morera-type theorems in the hyperbolic disc”, Izv. RAN. Ser. Mat., 82:1 (2018),  34–64  mathnet  elib; Izv. Math., 82:1 (2018), 31–60  isi  scopus
2. V. V. Volchkov, Vit. V. Volchkov, “An Analog of the Brown–Schreiber–Taylor Theorem for Weighted Hyperbolic Shifts”, Mat. Zametki, 103:2 (2018),  172–185  mathnet  elib; Math. Notes, 103:2 (2018), 175–186  isi  scopus
3. V. V. Volchkov, Vit. V. Volchkov, “A new characterization of holomorphic functions in the unit disk”, Probl. Anal. Issues Anal., 7(25):1 (2018),  134–147  mathnet  isi  elib
4. V. V. Volchkov, Vit. V. Volchkov, “Spectral synthesis on the group of conformal automorphisms of the unit disc”, Mat. Sb., 209:1 (2018),  3–36  mathnet  elib; Sb. Math., 209:1 (2018), 1–34  isi  scopus
2017
5. V. V. Volchkov, Vit.†V.†Volchkov, “Analogs of the Globevnik Problem on Riemannian Two-Point Homogeneous Spaces”, Mat. Zametki, 101:3 (2017),  359–372  mathnet  mathscinet  elib; Math. Notes, 101:3 (2017), 417–428  isi  scopus
2016
6. V. V. Volchkov, Vit.†V.†Volchkov, “Spectral analysis on the group of conformal automorphisms of the unit disc”, Mat. Sb., 207:7 (2016),  57–80  mathnet  mathscinet  elib; Sb. Math., 207:7 (2016), 942–963  isi  scopus
2015
7. V. V. Volchkov, Vit.†V.†Volchkov, “—Ónical injectivity sets of the Radon transform on spheres”, Algebra i Analiz, 27:5 (2015),  1–31  mathnet  mathscinet  elib; St. Petersburg Math. J., 27:5 (2016), 709–730  isi  scopus
8. V. V. Volchkov, Vit.†V.†Volchkov, I. M. Savost'yanova, “Description of the kernel of the generalized Minkowski transform on the sphere”, Izv. RAN. Ser. Mat., 79:1 (2015),  43–62  mathnet  mathscinet  zmath  elib; Izv. Math., 79:1 (2015), 40–59  isi  scopus
2014
9. V. V. Volchkov, Vit.†V.†Volchkov, “Local two-radii theorems on the multi-dimensional sphere”, Izv. RAN. Ser. Mat., 78:1 (2014),  3–24  mathnet  mathscinet  zmath  elib; Izv. Math., 78:1 (2014), 1–21  isi  scopus
2013
10. V. V. Volchkov, Vit.†V.†Volchkov, “Spherical means on two-point homogeneous spaces and applications”, Izv. RAN. Ser. Mat., 77:2 (2013),  3–34  mathnet  mathscinet  zmath  elib; Izv. Math., 77:2 (2013), 223–252  isi  scopus
2012
11. V. V. Volchkov, Vit. V. Volchkov, “Behaviour at infinity of solutions of twisted convolution equations”, Izv. RAN. Ser. Mat., 76:1 (2012),  85–100  mathnet  mathscinet  zmath  elib; Izv. Math., 76:1 (2012), 79–93  isi  scopus
2011
12. V. V. Volchkov, Vit.†V.†Volchkov, “On the extension problem for solutions of homogeneous convolution equations”, Izv. RAN. Ser. Mat., 75:3 (2011),  65–96  mathnet  mathscinet  zmath  elib; Izv. Math., 75:3 (2011), 507–537  isi  scopus
2010
13. V. V. Volchkov, Vit.†V.†Volchkov, “On a problem of Berenstein–Gay and its generalizations”, Izv. RAN. Ser. Mat., 74:4 (2010),  33–62  mathnet  mathscinet  zmath  elib; Izv. Math., 74:4 (2010), 691–721  isi  scopus
14. V. V. Volchkov, Vit.†V.†Volchkov, “Sets with the Pompeiu Property on the Plane and on the Sphere”, Mat. Zametki, 87:1 (2010),  69–82  mathnet  mathscinet  zmath  elib; Math. Notes, 87:1 (2010), 59–70  isi  scopus
2009
15. V. V. Volchkov, Vit. V. Volchkov, “Extremal problems related to the John uniqueness theorem”, Algebra i Analiz, 21:5 (2009),  37–69  mathnet  mathscinet  zmath; St. Petersburg Math. J., 21:5 (2010), 705–729  isi  scopus
2008
16. V. V. Volchkov, Vit.†V.†Volchkov, “Convolution equations in many-dimensional domains and on the Heisenberg reduced group”, Mat. Sb., 199:8 (2008),  29–60  mathnet  mathscinet  elib; Sb. Math., 199:8 (2008), 1139–1168  isi  scopus
2007
17. V. V. Volchkov, “Local two-radii theorem in symmetric spaces”, Mat. Sb., 198:11 (2007),  21–46  mathnet  mathscinet  zmath  elib; Sb. Math., 198:11 (2007), 1553–1577  isi  scopus
2006
18. V. V. Volchkov, “Uniqueness theorems for solutions of the convolution equation on symmetric spaces”, Izv. RAN. Ser. Mat., 70:6 (2006),  3–18  mathnet  mathscinet  zmath  elib; Izv. Math., 70:6 (2006), 1077–1092  isi  scopus
19. V. V. Volchkov, “A local two-radii theorem for quasianalytic classes of functions”, Mat. Zametki, 80:4 (2006),  490–500  mathnet  mathscinet  zmath  elib; Math. Notes, 80:4 (2006), 468–477  isi  scopus
2001
20. V. V. Volchkov, “A definitive version of the local two-radii theorem on hyperbolic spaces”, Izv. RAN. Ser. Mat., 65:2 (2001),  3–26  mathnet  mathscinet  zmath; Izv. Math., 65:2 (2001), 207–229  scopus
21. V. V. Volchkov, “Theorems on ball mean values in symmetric spaces”, Mat. Sb., 192:9 (2001),  17–38  mathnet  mathscinet  zmath; Sb. Math., 192:9 (2001), 1275–1296  isi  scopus
2000
22. V. V. Volchkov, “Extremal problems on Pompeiu sets. II”, Mat. Sb., 191:5 (2000),  3–16  mathnet  mathscinet  zmath; Sb. Math., 191:5 (2000), 619–632  isi  scopus
1999
23. V. V. Volchkov, “Injectivity sets for the Radon transform over a sphere”, Izv. RAN. Ser. Mat., 63:3 (1999),  63–76  mathnet  mathscinet  zmath; Izv. Math., 63:3 (1999), 481–493  isi  scopus
24. V. V. Volchkov, “Injectivity sets of the Pompeiu transform”, Mat. Sb., 190:11 (1999),  51–66  mathnet  mathscinet  zmath; Sb. Math., 190:11 (1999), 1607–1622  isi  scopus
1998
25. V. V. Volchkov, “Extremal problems on Pompeiu sets”, Mat. Sb., 189:7 (1998),  3–22  mathnet  mathscinet  zmath; Sb. Math., 189:7 (1998), 955–976  isi  scopus
1997
26. V. V. Volchkov, “Uniqueness theorems for some classes of functions with zero spherical means”, Mat. Zametki, 62:1 (1997),  59–65  mathnet  mathscinet  zmath; Math. Notes, 62:1 (1997), 50–55  isi
27. V. V. Volchkov, “Solution of the support problem for several function classes”, Mat. Sb., 188:9 (1997),  13–30  mathnet  mathscinet  zmath; Sb. Math., 188:9 (1997), 1279–1294  isi  scopus
1996
28. V. V. Volchkov, “An extremum problem related to Morera's theorem”, Mat. Zametki, 60:6 (1996),  804–809  mathnet  mathscinet  zmath; Math. Notes, 60:6 (1996), 606–610  isi
29. V. V. Volchkov, “Extremal cases of the Pompeiu problem”, Mat. Zametki, 59:5 (1996),  671–680  mathnet  mathscinet  zmath; Math. Notes, 59:5 (1996), 482–489  isi
30. V. V. Volchkov, “The final version of the mean value theorem for harmonic functions”, Mat. Zametki, 59:3 (1996),  351–358  mathnet  mathscinet  zmath; Math. Notes, 59:3 (1996), 247–252  isi
1995
31. V. V. Volchkov, “A definitive version of the local two-radii theorem”, Mat. Sb., 186:6 (1995),  15–34  mathnet  mathscinet  zmath; Sb. Math., 186:6 (1995), 783–802  isi
1994
32. V. V. Volchkov, “Theorems on two radii on bounded domains of Euclidean spaces”, Differ. Uravn., 30:10 (1994),  1719–1724  mathnet  mathscinet; Differ. Equ., 30:10 (1994), 1587–1592
33. V. V. Volchkov, “New two-radii theorems in the theory of harmonic functions”, Izv. RAN. Ser. Mat., 58:1 (1994),  182–194  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 44:1 (1995), 181–192  isi
34. V. V. Volchkov, “New mean value theorems for polyanalytic functions”, Mat. Zametki, 56:3 (1994),  20–28  mathnet  mathscinet  zmath; Math. Notes, 56:3 (1994), 889–895  isi
35. V. V. Volchkov, “Mean value theorems for a class of polynomials”, Sibirsk. Mat. Zh., 35:4 (1994),  737–745  mathnet  mathscinet  zmath; Siberian Math. J., 35:4 (1994), 656–663  isi
1993
36. V. V. Volchkov, “Morera-type theorems in domains with the weak cone condition”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, 10,  15–20  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 37:10 (1993), 13–18
37. V. V. Volchkov, “On a problem of Zalcman and its generalizations”, Mat. Zametki, 53:2 (1993),  30–36  mathnet  mathscinet  zmath; Math. Notes, 53:2 (1993), 134–138  isi
38. V. V. Volchkov, “New theorems on the mean for solutions of the Helmholtz equation”, Mat. Sb., 184:7 (1993),  71–78  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 79:2 (1994), 281–286  isi
1992
39. V. V. Volchkov, “Uniqueness theorems for multiple lacunary trigonometric series”, Mat. Zametki, 51:6 (1992),  27–31  mathnet  mathscinet  zmath; Math. Notes, 51:6 (1992), 550–552  isi

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