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Volchkov, Valerii Vladimirovich

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Total publications: 47
Scientific articles: 47

Number of views:
This page:3610
Abstract pages:13062
Full texts:3828
References:1314
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
2021
1. V. V. Volchkov, Vit. V. Volchkov, “Continuous extension of functions from a segment to functions in $\mathbb{R}^n$ with zero ball means”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, 3,  3–14  mathnet; Russian Math. (Iz. VUZ), 65:3 (2021), 1–11  isi  scopus
2020
2. V. V. Volchkov, Vit. V. Volchkov, “On the radial symmetry property for harmonic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, 10,  12–23  mathnet; Russian Math. (Iz. VUZ), 64:10 (2020), 9–19  isi  scopus
3. V. V. Volchkov, Vit. V. Volchkov, “On the problem of mean periodic extension”, Probl. Anal. Issues Anal., 9(27):2 (2020),  138–151  mathnet  isi  elib
4. V. V. Volchkov, Vit. V. Volchkov, “     ”, Sibirsk. Mat. Zh., 61:4 (2020),  752–764  mathnet
5. V. V. Volchkov, Vit. V. Volchkov, “Overdetermined Neumann boundary value problem in unbounded domains”, Ufimsk. Mat. Zh., 12:2 (2020),  10–20  mathnet; Ufa Math. J., 12:2 (2020), 10–20  isi
2018
6. V. V. Volchkov, Vit.V.Volchkov, “Morera-type theorems in the hyperbolic disc”, Izv. RAN. Ser. Mat., 82:1 (2018),  34–64  mathnet  mathscinet  elib; Izv. Math., 82:1 (2018), 31–60  isi  scopus
7. 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  mathscinet  elib; Math. Notes, 103:2 (2018), 175–186  isi  scopus
8. 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
9. 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  mathscinet  elib; Sb. Math., 209:1 (2018), 1–34  isi  scopus
2017
10. 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
11. 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
12. V. V. Volchkov, Vit.V.Volchkov, “nical 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
13. 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
14. 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
15. 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
16. 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
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. V. V. Volchkov, “Theorems on the injectivity of the Radon transform on spheres”, Dokl. Akad. Nauk, 354:3 (1997),  298–300  mathnet  mathscinet  zmath
32. 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
33. 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
34. V. V. Volchkov, “Two-radii theorems on spaces of constant curvature”, Dokl. Akad. Nauk, 347:3 (1996),  300–302  mathnet  mathscinet  zmath
35. 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
36. 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
37. 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
38. 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
39. V. V. Volchkov, “Approximation of functions on bounded domains in $R^n$ by linear combinations of shifts”, Dokl. Akad. Nauk, 334:5 (1994),  560–561  mathnet  mathscinet  zmath; Dokl. Math., 49:1 (1994), 160–162
40. 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
41. 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
42. 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
43. 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
44. 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
45. 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
46. 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
47. 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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