GENNADIY FELDMAN' s LIST OF PUBLICATIONS

THE BOOKS

  1. Characterization of Probability Distributions on Locally Compact Abelian Groups. Mathematical Surveys and Monographs, Vol. 273. American Mathematical Society, Providence, RI, 2023, 240 pp. 
  2. Characterization problems of mathematical statistics on locally compact Abelian groups. Kiev, Naukova Dumka, 2010, 432 pp. (Russian).
  3. Functional equations and characterization problems on locally compact Abelian groups. EMS Tracts in Mathematics Vol. 5. Zurich. European Mathematical Society (EMS), 2008, 268 pp.
  4. Arithmetic of probability distributions and characterization problems on Abelian groups AMS translation of mathematical monographs Vol. 116. Providence, RI: AMS 1993, 223 pp.
  5. Arithmetic of probability distributions and characterization problems on Abelian groups, Kiev , Naukova Dumka, 1990, 168 pp. (Russian).  

THE PAPERS

  1. Heyde Theorem on Locally Compact Abelian Groups with the Connected Component of Zero of Dimension 1. Potential Analysis, Vol. 60, No 4, article 160, (2024), 1445-1460. 
  2. Characterization of probability distributions on some locally compact Abelian groups containing an element of order 2. Journal of Mathematical Analysis and Applications, Vol. 539, No 2, article 128579, (2024), 16 pp. 
  3. Heyde Theorem for Locally Compact Abelian Groups Containing No Subgroups Topologically Isomorphic to the 2-Dimensional Torus. Journal of Fourier Analysis and Applications, Vol. 30, No 3, article 34 , (2024), 16 pp.
  4. Arithmetic of a certain convolution semigroup of probability distributions on the group R × Z(2). Journal of Mathematical Physics, Analysis, Geometry, Vol.  20, No 4, (2024), 448-460.
  5. On a characterization theorem in the space  Rn. Journal of Mathematical Analysis and Applications, Vol. 528, No 2, article 127583, (2023), 12 pp.
  6. On a Characterization of Shifts of Haar Distributions on Compact Open Subgroups of a Compact Abelian Group. Results in Mathematics, Vol. 78, No 4, article 160, (2023), 22 pp.
  7. On a characterization theorem for locally compact Abelian groups containing an element of order 2. Potential Analysis. 2022, Vol. 56, No 2, (2022), 297–315.
  8. Generalization of the Heyde theorem to some locally compact Abelian groups. Results in Mathematics. Vol. 77, No 4, article 177, (2022), 1–20.
  9. On the Skitovich–Darmois theorem for complex and quaternion random variables. Georgian Mathematical Journal. Vol. 28, No 5, (2021), 717- 723
  10. A characterization theorem on compact Abelian groups. Journal of Fourier Analysis and Applications. Vol. 27, No 5, article 86, (2021), 23 pp.
  11. The Kac–Bernstein functional equation on Abelian groups. Aequationes Mathematicae, Vol. 95, No 4, (2021), 737-750.
  12. Generalized Pólya’s Theorem on a-adic Solenoids, Results in Mathematics, Vol. 76, No 3, article 124, (2021), 11 pp.
  13. On a Characterization Theorem for Connected Locally Compact Abelian Groups. Journal of Fourier Analysis and Applications. Vol. 26, No 1, article 14, (2020), 22 pp.
  14. On Heyde’s Theorem on the Group R×T. Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, Vol. 493, (2020), 42–46 (Russian), (English trans. Doklady Mathematics, Vol. 102, No 1, (2020), 296-300.
  15. On a generalisation of the Skitovich–Darmois theorem for several linear forms on Abelian groups. Aequationes Mathematicae, Vol. 94, No 2, (2020), 369-380.
  16. On a characterization theorem on a-adic solenoids. Dokl. Akad. Nauk, Vol. 489, No 3, (2019), 227-231 (Russian), (English trans. Doklady Mathematics, Vol. 100, No 3, (2019)), 538-541.
  17. On a characterization theorem on non-discrete totally disconnected locally compact fields. Publ. Math. Debrecen . Vol. 95, No 3-4, (2019), 363-376 (with M.V. Myronyuk).
  18. On a C.R. Rao’s Theorem for Locally Compact Abelian Groups. Dokl. Akad. Nauk, Vol. 484, No 3, (2019), 273–276 (Russian), (English trans. Doklady Mathematics, Vol. 99, No 1, (2019), 48-51).
  19. On analogues of C.R. Rao's theorems for locally compact Abelian groups. J. Difference Equat. Appl., Vol. 12, No 12, (2018), 1967--1980.
  20. On Heyde’s Theorem for Probability Distributions on a Discrete Abelian Group. Dokl. Akad. Nauk, Vol. 478, No 1, (2018), 17–21 (Russian), (English trans. Doklady Mathematics, Vol. 97, No 1, (2018), 11-14).
  21. On the Skitovich--Darmois theorem for some locally compact Abelian groups. Aequationes Mathematicae, Vol. 92, No 6, (2018), 1129--1147 (with M.V. Myronyuk).
  22. On a characterisation theorem for probability distributions on discrete Abelian groups. Teor. Veroyatn. Primen., Vol. 63, No 4, (2018), 730–754 (Russian), (English trans. Theory Probab. Appl. Vol. 63, No 4, (2019), 594-612).
  23. On the Heyde theorem for some locally compact Abelian groups. Dokl. Akad. Nauk, Vol. 473, No 3, (2017), 16–20 (Russian), (English trans. Doklady Mathematics, Vol. 95, No 2, (2017), 147-150).
  24. Heyde's characterization theorem for some locally compact Abelian groups. Teor. Veroyatn. Primen., Vol. 62, No 3, (2017), 499–517 (Russian). (English trans. Theory Probab. Appl. Vol. 62, No 4, (2018), 399-412).
  25. On a Characterization of Idempotent Distributions on Discrete Fields and on the Field of p-Adic Numbers. Journal of Theoretical Probability, Vol. 30, No 2 (2017), 608-623 (with M.V. Myronyuk).
  26. Characterization theorems for Q-independent random variables with values in a locally compact Abelian group. Aequationes Mathematicae, Vol. 91, No 5 (2017), 949-967
  27. On Geary’s theorem for the field of p-adic numbers. Dokl. Akad. Nauk, Vol. 467, No 2, (2016), 131–134 (Russian), (English trans. Doklady Mathematics, Vol. 93, No 2, (2016), 152-154) (with M.V. Myronyuk).
  28. Independent random variables in Abelian groups with independent sum and difference. Teor. Veroyatn. Primen., Vol. 61, No 2, (2016), 404–414 (Russian) (English trans. Theory Probab. Appl. Vol. 61, No 2, (2017), 335-345).
  29. On a characterization theorem for the group of p-adic numbers. Publ. Math. Debrecen, Vol. 87,  No 1-2,  (2015),  147-166.
  30. On the Skitovich–Darmois theorem for the group of p -adic numbers. J. of Theor. Probab., Vol. 28 , No 2, (2015), 539-549.
  31. On a functional equation appearing in characterization of distributions by the optimality of an estimate.
    Aequationes Mathematicae, Vol. 86, No 3, (2015), 663-671 (with P. Graczyk).
  32. Independent linear statistics on the cylinders. Teor. Veroyatn. Primen., Vol. 59, No 2, (2014), 252–275 (Russian), (English trans. Theory Probab. Appl. Vol. 59, No 2, (2015), 260-278) (with M.V. Myronyuk).
  33. The Heyde theorem on the group of p-adic numbers.  Dokl. Akad. Nauk, Vol. 456, No 5, (2014), 528–531 (English trans. Doklady Mathematics, Vol. 89, No 3, (2014), 359–361).
  34. On a characterization of a convolutions of Gaussian and Haar distributions. Mathematische Nachrichten, Vol. 286, No 4, (2013), 340–348.
  35. On a characterization of a convolution of Gaussian and idempotent distributions. Dokl. Akad. Nauk, Vol. 449, No 4, (2013), 398–401 (English trans. Doklady Mathematics, Vol. 87, No 2, (2013), 198–201).
  36. Gaussian measures in the sense of Bernstein: factorization, supports, zero-one low. Teor. Veroyatn. Primen., Vol. 56, No 3, (2011), 494–513 (Russian), (English trans. Theory Probab. Appl. Vol. 56, No 3, (2012), 359–375).
  37. Gaussian distribution in the sense of Bernstein on locally compact Abelian groups. Dokl. Akad. Nauk, Vol. 440, No 3, (2011), 314–316 (English trans. Doklady Mathematics, Vol. 84, No 2, (2011), 653–655).
  38. Independent linear forms on connected Abelian groups. Mathematische Nachrichten, Vol. 284, No 2–3, (2011), 255-265 (with M.V. Myronyuk).
  39. On a characterization theorem on Abelian groups , Publ. Math. Debrecen . Vol. 77, No 3-4, (2010), 383-398 (with M.V. Myronyuk).
  40. The Skitovich-Darmois theorem for locally compact Abelian groups, J. of the Australian Mathematical Society, Vol. 88, No 3, (2010), 339-352 (with P. Graczyk).
  41. The Heyde theorem for locally compact Abelian groups. J . of Functional Analysis, Vol. 258, No 12, (2010), 3977-3987.
  42. Independent linear statistics on a-adic solenoids. Teor. Veroyatn. Primen., Vol. 54, No 3, (2009), 515–532 (Russian), (English trans. Theory Probab. Appl. Vol. 54, No 3, (2010), 375-388 ).
  43. On the Skitovich-Darmois theorem for connected Abelian groups. Dokl. Akad. Nauk, Vol. 424, No 1, (2009), 12–15 (Russian), (English trans. Doklady Mathematics, Vol. 79, No 1, (2009), 6–9) (with M.V. Myronyuk).
  44. On a theorem of K. Schmidt. Bull. Lond. Math. Soc, Vol. 41 , No 1, (2009), 103–108.
  45. The Skitovich-Darmois equation in the classes of continuous and measurable functions. Aequationes Mathematicae Vol. 75, No 1–2, (2008), 75–92 (with M.V. Myronyuk).
  46. Independent linear statistics on a-adic solenoids. Dokl. Akad. Nauk, Vol. 417, No 4, (2007), 464–467 (Russian), (English trans. Doklady Mathematics, Vol. 76, No 3, (2007), 904–907).
  47. Continuity properties of polynomials on locally compact abelian groups. Aequationes mathematicae, Vol. 73, No 3, (2007), 285–290.
  48. Independent linear statistics on the two-dimensional torus. Teor. Veroyatn. Primen., Vol. 52, No 1, (2007), 3–20 (Russian), (English trans. Theory Probab. Appl. Vol. 52, No 1, (2008), 78–92) (with M.V. Myronyuk).
  49. The Skitovich-Darmous equation in the classes of continuous and measurable functions. Dokl. Akad. Nauk, Vol. 410, No 4, (2006),   453–456 (Russian), (English trans. Doklady Mathematics, Vol. 74, No 2, (2006),   700–703) (with M.V. Myronyuk ).
  50. On the Heyde theorem for discrete Abelian groups. Studia Math. Vol., 177 , No 1, (2006),   67–79.
  51. On a characterization theorem for locally compact abelian groups. Probab. Theory Relat. Fields, Vol. 133, (2005),   345–357.
  52. On the Skitovich-Darmos theorem on the two-dimensional torus. Dokl. Akad. Nauk, Vol. 401, No 6, (2005),   741–743 (Russian), (English trans. Doklady Mathematics, Vol. 71, No 2, (2005),   274–276) ) (with M.V. Myronyuk ).
  53. On a characterization theorem on finite Abelian groups. Sibirsk. Mat. Zh., Vol. 46, No 2, (2005)   403– 415 (Russian), (English trans. Siberian Math. J., Vol. 4 6, (2005),   315– 324) (with M.V. Myronyuk ).
  54. On the Heyde theorem for finite Abelian groups. J. of Theoretical Probability, Vol. 17, No 4, (2004),   929–941.
  55. On the Skitovich-Darmois theorem for discrete Abelian groups. Teor. Veroyatn. Primen., Vol. 49, No 3, (2004),   596–601 (Russian), (English trans. Theory Probab. Appl. Vol. 49, No 3, (2005), 527–531) (with P. Graczyk).
  56. On a characterization theorem on finite Abelian groups. Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki. No 4 (2004 ),   23–27 (Russian) (with M.V. Myronyuk ).
  57. A characterization of the Gaussian distribution on Abelian groups. Probab. Theory Relat. Fields, Vol. 126, No 1 (2003),   91–102.
  58. To a characterization of the Gaussian distributins on Abelian groups. Dokl. Akad. Nauk, Vol. 384, No 6, (2002),   738–740 (Russian), (English trans. Doklady Mathematics, Vol. 65, No 3, (2002),   440–442).
  59. On non-quasianalytic representations of Abelian groups. Matematicheskaya Fizika, Analiz,  Geometriya, Vol. 9, No 1, (2002),   101–106 (with Quoc-Phong Vu ).
  60. On groups for which the Bernstein characterization of a Gaussian distribution is valid. Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki. No 8 (2001),   29–31.
  61. Independent linear statistics on finite Abelian groups. Ukrain. Mat. Zh., Vol. 53, No 4, (2001),   441–448 (Russian), (English trans. Ukrainian Math. J., Vol. 53, No 4, (2001),   499–506) (with P. Graczyk).
  62. On the Skitovich–Darmois Theorem for Compact Abelian Groups. J. of Theoretical Probability, Vol. 13, No 3, (2000),   859–869 (with P. Graczyk).
  63. More on the Skitovich-Darmois theorem for finite Abelian groups. Teor. Veroyatn. Primen., Vol. 45, No 3, (2000),   603–607 (Russian), (English trans. Theory Probab. Appl. Vol. 45, No 3, (2001),   507–511).
  64. A stability of one property for probability measures on Abelin groups. Statistic and Probability Letters, Vol. 49, (2000),   39–44 (with H.Carnal).
  65. On a property of entire characteristic functions of finite order with real zeros. Dokl. Akad. Nauk, Vol. 366, No 2, (1999),   162–163 (Russian), (English trans. Doklady Mathematics, Vol. 59, No 3, (1999),   379–380) (with H.Carnal).
  66. On an isometric representation with the maximal set of spectral subspaces. Matematicheskaya Fizika, Analiz,  Geometriya, Vol. 5, No 3/4, (1998),   297–303 (with G. Muraz).
  67. On a characterization of Gaussian distributions on Abelian groups by constancy of regression. Teor. Veroyatn. Primen., Vol. 43, No 3, (1998),   606–610 (Russian), (English trans. Theory Probab. Appl. Vol. 43, No 3, (1999),   477–480).
  68. The Skitovich-Darmois theorem for discrete periodic Abelian groups. Teor. Veroyatn. Primen., Vol. 42, No 4, (1997,   747–756 (Russian), (English trans. Theory Probab. Appl. Vol. 42, No 4, (1998),   611–617).
  69. Phase retrial for probability measures on Abelian groups, II. J. of Theoretical Probability, Vol. 10, No 4, (1997),   1065–1074 (with H.Carnal).
  70. Measures on Abelian groups. Trudy S.-Petersgurgskogo Mat. Obschestva, Vol. 4, (1996),   113–156, (Russian), (English trans. Amer. Math. Soc. transl. (2) Vol. 188, (1999),   75–103.
  71. On the Skitovich-Darmois theorem on compact groups. Teor. Veroyatn. Primen., Vol. 41, No. 4, (1996),   900–906 (Russian), (English trans. Theory Probab. Appl. Vol. 41, (1997), No. 4, 768–773).
  72. Phase retrial for probability measures on Abelian groups. J. of Theoretical Probability, Vol. 8, No 3, (1995),   717–725 (with H.Carnal).
  73. On a characterization theorem for the Cauchy distribution on abelian groups. Sibirsk. Mat. Zh., Vol. 36, No 1, (1995)   215–221 (Russian), (English trans. Siberian Math. J., Vol. 36, (1995),   196–201).
  74. On the Skitovich-Darmois theorem on Abelian groups. Teor. Veroyatn. Primen., Vol. 37, No. 4, (1992),   695–708 (Russian), (English trans. Theory Probab. Appl. Vol. 37, (1993), No. 4,  621–631).
  75. Cauchy distribution on Abelian groups and its characterization. Teor. Veroyatn. Primen., Vol. 36, No. 4, (1991),   711–723, (Russian), (English trans. Theory Probab. Appl. Vol. 36, (1992), No. 4,  670–681).
  76. On an analogue for groups of a theorem of A. Ya. Khinchin . Analytic methods in probability theory and operator theory , Kiev, Naukova Dumka, (1990) , 21–25 (Russian).
  77. Characterization of the Gaussian distribution on groups by the independence of linear statistics. Sibirsk. Mat. Zh, Vol. 31, No 2, (1990),   180–190, (Russian), (English trans. Siberian Math. J., Vol. 31, (1990),   336–345). pdf
  78. Groups admitting a characterization of the Gaussian distribution by the equidistribution of a monomial and linear statistics. Ukrain. Mat. Zh. Vol. 42, No 1, (1990),   139–142 (Russian), (English trans. Ukrainian Math. J. Vol. 42, (1990),   125–128).
  79. The Cauchy distribution on Abelian groups and its characterization. Dokl. Akad Nauk SSSR, Vol. 309, No 1, (1989),   46–49 (Russian), (English trans. Soviet Math. Dokl. Vol. 40, (1990), 486–489).
  80. Characterizing the Gaussian distribution on groups by the uniform distribution of a monomial and linear statistics. Ukrain. Mat. Zh. Vol. 41, No 8, (1989), 1112–1118 (Russian), (English trans. Ukrainian Math. J. Vol. 41, No 8, (1989), 959–963).
  81. Marcinkiewicz and Lukacs theorems on abelian groups. Teor. Veroyatn. Primen.,Vol. 34, No. 2, (1989),   330–339 (Russian), (English trans. Theory Probab. Appl. Vol. 34, (1990), No. 2,  290–297). pdf
  82. Characterizing the Gaussian distribution on groups by the uniform distribution of a monomial and linear statistics. Ukrain. Mat. Zh. Vol. 41, No 8, (1989), 1112–1118 (Russian), (English trans. Ukrainian Math. J. Vol. 41, No 8, (1989, 959–963).
  83. Gaussian measures in Urbanik's sense and a characterization theorem for Abelian groups. Studia math., Vol. 90, (1988),   165–174.
  84. On a characterization of the Gaussian distribution on Abelian groups. Teor. Veroyatn. Primen., Vol. 32, No. 3, (1987),  623–626 ( Russian), (English trans. Theory Probab. Appl. Vol. 32, (1988), No. 3,  565–569).
  85. The Polya characterization of a Gaussian measures on groups. Studia math., Vol. 87, (1987),   9–21.
  86. Bernstein Gaussian distributions on groups. Teor. Veroyatn. Primen., Vol. 31, No. 1, (1986),   47–58 (Russian), (English trans. Theory Probab. Appl. Vol. 31, (1987), No. 1,   40–49).
  87. On infinitely divisible distributions of the class I0 on groups. Teor. Veroyatn. Primen., Vol. 30, No. 3, (1985),   449– 461 ( Russian), (English trans. Theory Probab. Appl. Vol. 30, (1986), No. 3,  475–484).
  88. Generalized Poisson distribution of class  I0 on groups. Teor. Veroyatn. Primen., Vol. 29, No. 2, (1984),   222–233 ( Russian), (English trans. Theory Probab. Appl. Vol. 29, (1985), No. 2,  218–230).
  89. Generalized Poisson distribution on groups. Funkts. Anal. Prilozh., Vol. 17, No 1, (1983),   81–82 (Russian), (English trans. Funct. Anal. Appl., Vol. 17, (1983),   72–74).
  90. On the decomposition of the convolution of a Gaussian and Poisson distribution on locally compact Abelian groups. J. of Mult. Analysis, Vol. 13, No 1, (1983),   148–166, (with A.E.Fryntov).
  91. On Urbanik's characterization of Gaussian measures on locally compact Abelian groups. Studia Math., Vol. 73, (1982),   81–86.
  92. On a decomposition of generalized Poisson distributions on groups. Teor. Veroyatn. Primen., Vol. 27, No. 4, (1982),   725–738, (Russian), (English trans. Theory Probab. Appl. Vol. 27, (1983), No. 4,  780–794).
  93. Decomposition of the convolution of two Poisson distributions on a locally compact Abelian group. Teor. Veroyatn. Primen., Vol. 26, No. 3, (1981),   612–618 (Russian), (English trans. Theory Probab. Appl. Vol. 26, (1982), No. 3,  601–607) (with A.E.Fryntov).
  94. Expansion of a convolution of gaussian and poisson distributions of locally compact Abelian groups . Funkts. Anal. Prilozh., Vol. 13, No 4 , (1979),   93–94 (Russian), ( English trans. Funct. Anal. Appl., Vol. 13, (1979), 316–317) (with A.E.Fryntov).
  95. Gaussian distributions on locally compact Abelian groups. Teor. Veroyatn. Primen., Vol. 23, No. 3, (1978),   548–563 ( Russian), ( English trans. Theory Probab. Appl. Vol. 23, (1979), No. 3,  529–542).pdf
  96. On generalized Poisson distributions on groups. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), Vol.72, (1977),   161–185 (Russian), ( English trans. J. Soviet math. Vol. 23, No 3, (1984),  2335–2351 ).
  97. On the decomposition of Gaussian distributions on groups. Teor. Veroyatn. Primen., Vol. 22, No. 1, (1977),   136–143 (Russian), (English trans. Theory Probab. Appl., Vol. 22, (1977), No. 1,  133–140).
  98. Gaussian distributions on locally compact Abelian groups. Funkts. Anal. Prilozh., Vol. 11, No 1, (1977,   85–86 (Russian), (English trans. Funct. Anal. Appl., Vol. 11, (1977),   76–78).
  99. On generalized Poisson distributions on groups. Teor. Veroyatn. Primen., Vol. 20, No 3, (1975),  653–656 (Russian), (English trans. Theory Probab. Appl., Vol. 20, (1976), No. 3,  641–644).
  100. The spectrum of contractions that depend analytically on a parameter . Uspehi Mat. Nauk , Vol. 29, No 6, (1974),   179–180 (Russian).
  101. The semisimplicity of an algebra generated by an isometric operator.Funkts. Anal. Prilozh., Vol. 8, No 2, (1974),   93–94 (Russian), (English trans. Funct. Anal. Appl., Vol. 8, (1974),   182–183).
  102. On representations with a separable spectrum. Funkts. Anal. Prilozh., Vol. 7, No 2 , (1973),   52–61 (Russian), (English trans. Funct. Anal. Appl., Vol. 7, (1973),   129–136) (with Yu.I.Ljubich and V.I. Macaev).
  103. Harmonic analysis of nonunitary representations of locally compact abelian groups . Teor. Funkts. Funkts. Analiz Prilozh., Vol.17, (1973),   169–183 (Russian)
  104. On isometric representations of locally compact abelian groups. Dokl. Akad. Nauk SSSR, vol. 207, (1972), No 5,   1063–1065 (Russian), (English trans. Soviet Math. Dokl. Vol. 12, (1973), 1688–1692).
  105. Spectral subspaces of a nonquasianalytic operator . Mat. Fizika Funkts. Anal., Vol. 3, (1972),  81– 87 (Russian).
  106. The property of being a basis of a system of proper subspaces of an isometric representation . Mat. Fizika Funkts. Anal., Vol. 3, (1972), 77–88 (Russian).
  107. Spectral theory of representations of locally compact abelian groups. Funkts. Anal. Prilozh., Vol. 6, No 1, (1972),   89 (Russian), (English trans. Funct. Anal. Appl., Vol. 6, (1972),   82–83)
  108. On the separability of the spectrum of a representation of a locally compact abelian groups. Dokl. Akad.Nauk SSSR, Vol. 201, No 6, (1971),   1282–1284 (Russian), (English trans. Soviet Math. Dokl. Vol. 12, No 6, (1971),   1824–1827) (with Ju.I.Ljubich and V.I. Macaev).
  109. Zeros of functions in W+ . Teor. Funkts. Funkts. Analiz Prilozh., Vol. 13, (1971),   108–112 (Russian) (with V.E.Katsnelson).
  110. Primary ideals of the algebra W+ . Teor. Funkts. Funkts. Analiz Prilozh., Vol. 11, (1970),   108–118 (Russian).