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Rogov, Voldemar-Berenkard Konstantinovich

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Total publications: 18
Scientific articles: 17

Number of views:
This page:538
Abstract pages:5957
Full texts:1780
References:460
Professor
Doctor of physico-mathematical sciences (1990)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 23.06.1938
E-mail:
Keywords: Lie groups; homogeneous spaces; harmonic analysis; quantum groups; noncommutative analysis; dynamical system.

Subject:

The description of the eigenfunctions of the Beltrami-Laplace operator on the arbitrary homogeneous pseudo-Riemannian symmetric space of rank 1. In general the Beltrami–Laplace operator is ultrahyperbolic one in this case. The integral Fourier–Mellin–Whittaker transform transforming the Beltrami–Laplace operator in the horosperical coordinates to the ordinary differential operator was constructed. The inversion formula was received. The number of papers (with M. A. Olshanetsky) were devoted to the integral representations of the modified $q$-Bessel functions and $q$-Macdonald functions. The $q$-Fourier transform and the inversion formula were constructed in the space of the distributions. The $q$-convolution and its $q$-Fourier transform are defined. The unitary irreducible representations of the quantum Lorentz group are constructed and their connection with the quantum relativistic Toda chain is determined.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1965 (department of theory of functions and functional analysis). Ph.D. thesis was defended in 1972. D.Sci. thesis was defended in 1990.

   
Main publications:
  • Rogov V.-B. K. $q^2$-Convolution and its $q^2$-Fourier transform // Czechoslovk Journal of Physics, 2000, 50(11), 1347–1352.

http://www.mathnet.ru/eng/person8472
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/234910

Publications in Math-Net.Ru
2005
1. M. A. Olshanetsky, V.-B. K. Rogov, “dS–AdS Structures in Noncommutative Minkowski Spaces”, TMF, 144:3 (2005),  513–543  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 144:3 (2005), 1315–1343  isi
2003
2. V. K. Rogov, “Integral representations of $q$-Macdonald functions”, Mat. Sb., 194:2 (2003),  117–128  mathnet  mathscinet  zmath; Sb. Math., 194:2 (2003), 281–293  isi  scopus
2002
3. M. A. Olshanetsky, V.-B. K. Rogov, “Unitary Representations of the Quantum Lorentz Group and Quantum Relativistic Toda Chain”, TMF, 130:3 (2002),  355–382  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 130:3 (2002), 299–322  isi
1999
4. M. A. Olshanetsky, V.-B. K. Rogov, “The $q$-Fourier transformation of $q$-generalized functions”, Mat. Sb., 190:5 (1999),  93–112  mathnet  mathscinet  zmath; Sb. Math., 190:5 (1999), 717–735  isi  scopus
1997
5. M. A. Olshanetsky, V.-B. K. Rogov, “$q$-integral representations of modified $q$-Bessel functions and $q$-Macdonald functions”, Mat. Sb., 188:8 (1997),  125–148  mathnet  mathscinet  zmath  elib; Sb. Math., 188:8 (1997), 1235–1258  isi  scopus
1996
6. M. A. Olshanetsky, V.-B. K. Rogov, “Modified $q$-Bessel functions and $q$-Macdonald functions”, Mat. Sb., 187:10 (1996),  109–128  mathnet  mathscinet  zmath; Sb. Math., 187:10 (1996), 1525–1544  isi  scopus
1992
7. V. K. Rogov, “Eigenfunctions of the Beltrami–Laplace operator on homogeneous pseudo-Riemannian symmetric spaces of rank 1”, Mat. Sb., 183:3 (1992),  95–132  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 75:2 (1993), 371–404  isi
1989
8. V. K. Rogov, “The Fourier–Mellin–Whittacker transform on horospheres of homogeneous pseudo-riemannian symmetric space of rank 1”, Mat. Sb., 180:3 (1989),  336–353  mathnet  mathscinet  zmath; Math. USSR-Sb., 66:2 (1990), 343–361  isi
1988
9. V.-B. K. Rogov, “Fourier transform on the orispheres of homogeneous pseudo-Riemannian symmetric spaces of rank 1”, Funktsional. Anal. i Prilozhen., 22:2 (1988),  89–91  mathnet  mathscinet  zmath; Funct. Anal. Appl., 22:2 (1988), 161–163  isi
1987
10. V.-B. K. Rogov, “Spaces dual relative to the Mellin–Whittaker integral transform”, Mat. Zametki, 42:6 (1987),  810–818  mathnet  mathscinet  zmath; Math. Notes, 42:6 (1987), 944–949  isi
11. M. A. Olshanetsky, V.-B. K. Rogov, “Adjoint representations of exceptional Lie algebras”, TMF, 72:1 (1987),  3–11  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 72:1 (1987), 679–685  isi
1986
12. V.-B. K. Rogov, “The Mellin-Whittaker integral transform”, Mat. Zametki, 39:6 (1986),  798–805  mathnet  mathscinet  zmath; Math. Notes, 39:6 (1986), 434–437  isi
1980
13. V.-B. K. Rogov, “Beltrami-Laplace operator on homogeneous symmetric spaces of rank 1”, Mat. Zametki, 28:1 (1980),  59–66  mathnet  mathscinet  zmath; Math. Notes, 28:1 (1980), 493–497  isi
1977
14. V. K. Rogov, “On the eigenfunctions of the Beltrami–Laplace operator on homogeneous symmetric spaces of rank 1”, Mat. Sb. (N.S.), 104(146):2(10) (1977),  292–313  mathnet  mathscinet  zmath; Math. USSR-Sb., 33:2 (1977), 261–280  isi
1975
15. V.-B. K. Rogov, “Factor space of functions with a singularity”, Mat. Zametki, 18:2 (1975),  279–290  mathnet  mathscinet  zmath; Math. Notes, 18:2 (1975), 753–7599
1971
16. V. K. Rogov, “Eigenfunctions of the Beltrami–Laplace operator on hyperbo”, Uspekhi Mat. Nauk, 26:3(159) (1971),  207–208  mathnet  mathscinet  zmath
1970
17. V.-B. K. Rogov, “Eigenfunctions of the Beltrami–Laplace operator on a hyperboloid of one sheet”, Mat. Zametki, 7:2 (1970),  255–263  mathnet  mathscinet  zmath; Math. Notes, 7:2 (1970), 152–157

1991
18. F. I. Karpelevich, A. U. Klimyk, L. M. Koganov, M. A. Olshanetsky, V.-B. K. Rogov, A. I. Rubinshtein, Ya. A. Smorodinskii, “Naum Yakovlevich Vilenkin (on his seventieth birthday)”, Uspekhi Mat. Nauk, 46:3(279) (1991),  215–217  mathnet  mathscinet  zmath; Russian Math. Surveys, 46:3 (1991), 251–254  isi

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