Kosyak Oleksandr
Publications
Monograph:
Kosyak A.V. Regular, quasiregular and induced representations of infinite-dimensional groups, EMS (Europ. Math. Soc) Tracts in Mathematics 29, 587 p. 2018. https://doi.org/10.4171/181
Research papers:
Kosyak A.V. and Samoilenko Yu.S. On families of commuting self-adjoint operators, {\it Ukrain. Math. Journ.} 1979, v.31, no.5, p.555-558.
Kosyak A.V. Garding domain and entire vectors for inductive limits of Abelian locally-compact groups, {\it Ukrain. Math. Journ.} 1983, v.35, no. 4, p.427-434.
Kosyak A.V. Garding domain for representations of canonical commuting relations, {\it Ukrain. Math. Journ.} 1984, v.36, no.6, p.709-715.
Kosyak A.V. Extension of unitary representations of inductive limits of finite-dimensional Lie groups, {\it Rep. Math. Phys.} 1988, v.26, no.2, p.129-148.
Kosyak A.V. Irreducibility criterion for regular Gaussian representations of
group of finite upper-triangular matrices, {\it Funct. Anal. i Priloz.} 1990, v.24, issue 3, p.82-83.
Kosyak A.V. and Samoilenko Yu.S. Quasi-invariant measures on { \it Large} groups. {\it Selecta Math. Sov.} 1991, v.10, no.1, p.1-6 .
Kosyak A.V. Criteria for irreducibility and equivalence of regular Gaussian representations of group of finite upper-trianguler matrices of infinite order, {\it Selecta Math. Sov.} 1992, v.11, no.3, p.241-291.
Kosyak A.V. Irreducible regular Gaussian representations of the group of the interval and circle diffeomorphisms, {\it Journ. Funct. Anal.} 1994, v.125, p.493-547.
Kosyak A.V. and Zekri R. Type of von Neumann algebras generated by regular representations of infinite dimensional groups.{\it Vestnik Tambov Univ.} 1998, vol. 3, issue 1, 47-48.
Kosyak A.V. Measures on infinite-dimensional groups quasi-invariant with respect to inverse mapping and the commutant theorem, Analysis on infinite-dimensional Lie groups and algebras (Marseille, 1997),182-196, World Sci. Publishing, River Edge, NJ, 1998.
Kosyak A.V. and Zekri R. Anti-Wick symbols on infinite tensor product spaces.
{\it Methods of Funct. Anal. and Topology}. 1999, v.5, No 2, p.29-39.
Kosyak A.V. Inversion-quasi-invariant Gaussian measures on the group of
infinite-order upper-triangular matrices. {\it Funct. Anal. i Priloz. 2000,} v.34, issue 1, p.86-90.
Kosyak A.V. and Zekri R. Regular representations of infinite-dimensional groups and factors, I. {\it Methods of Funct. Anal. and Topology.} 2000, v.6, No 2, p. 50-59.
Kosyak A.V. Regular representations of the group of finite upper-triangular matrices, corresponding to product measures and criteria for their irreducibility. {\it Methods of Funct. Anal. and Topology.} 2000, v.6, No 4, p.43-56.
Kosyak A.V. Elementary representations of the group $B_0^{\Bbb N}$ I. {\it Methods of Funct. Anal. and Topology.} 2001, v.7, No 1, p.34-44.
Kosyak A.V. Irreducibility of the regular Gaussian representations of the group $B_0^{\mathbb Z}$. {\it Methods of Funct. Anal. and Topology.} 2001, v.7, No 2, p.42-51.
Kosyak A.V. and Zekri R. Regular representations of infinite-dimensional group $B_0^{\mathbb Z}$ and factors. {\it Methods of Funct. Anal. and Topology.} 2001, v.7, No 4, p.43 - 48 (co-author R.Zekri)
Kosyak A.V. Elementary representations of the group $B_0^{\Bbb Z}$. I. {\it Ukrain. Math. Journ.} 2002, v.54, No 2, p.205-215.
Kosyak A.V. Generalized Ismagilov conjecture for the group $B_0^{\Bbb N}$. I.{\it Methods of Funct. Anal. and Topology.} 2002, v.8, No 2, p.33-49.
Kosyak A.V. Generalized Ismagilov conjecture for the group $B_0^{\Bbb N}$. II.{\it Methods of Funct. Anal. and Topology.} 2002, v.8, No 3, p.27-45.
Kosyak A.V. and L\'eandre R. Regular Representations of the Central Extension of the Group of Diffeomorphisms of a Circle. {\it Doklady Mathematics.} 2002, v.66, No 1, p.75-77 . From {\it Doklady Akademii Nauk}, v.385, No 4, p.453-455
Kosyak A.V. Irreducibility criterion for quasiregular representations of the group of finite upper-trianguler matrices. {\it Funct. Anal. i Priloz.} 2003, v.37, issue 1, p.78-81.
Kosyak A.V. and Zekri R. Anti - Wick symbols for infinite products in K-homology, {\it K-theory.} 2003, v. 29 117-145.
Kosyak A.V. Quasi-invariant measures and irreducible representations of the inductive limit of special linear groups. {\it Functional Analysis and Its Applications}, Vol. 38, No 1, pp.67-68, 2004.
Kosyak A. and Albeverio S. Quasi-regular representations of the infinite-dimensional Borel group. {\it Journ. Funct. Anal.} v. 218, issue 2 (2005) 445-474.
Kosyak A.V. and Nizhnik L.P. Generalized translation operators and hipergroups constructed from self-adjoint operators, {\it Ukrain. Math. Journ.} 2005, v.57, no.5, p.659-669.
Kosyak A. and Albeverio S. Group action, quasi-invariant measures and quasiregular representations of the infinite-dimensional nilpotent group, {\it Contemporary Mathematics of AMS}. 2005, v.385, 259-280. 364 p.
Kosyak A. and Albeverio S. Quasiregular representations of the infinite-dimensional nilpotent group, {\it J. Funct. Anal.} 236 (2006) 634-681.
A. V. Kosyak, A. Yu. Khrennikov, V. M. Shelkovich, Pseudodifferential operators on adele rings and wavelet bases. Doklady Mathematics, 85, 358–362 (2012). https://doi.org/10.1134/S1064562412030167
A. V. Kosyak, A. Yu. Khrennikov, V. M. Shelkovich, Wavelet bases on adele rings, Doklady Mathematics, 85, 75–79 (2012). https://doi.org/10.1134/S1064562412010267
A. Yu. Khrennikov, A.V. Kosyak, V.M. Shelkovich Wavelet analysis on adeles and pseudo-differential operators, Journal of Fourier Analysis and Applications 18 (6), (2012) 1215-1264. https://doi.org/10.1007/s00041-012-9233-6
A.V. Kosyak, Induced representations of infinite-dimensional groups, I. J. Funct. Anal. 266 (6) (2014) 3395-3434. https://doi.org/10.1016/j.jfa.2014.01.008
A.V. Kosyak, Criteria of irreducibility of the Koopman representations for the group ${\rm GL}_0(2\infty,\mathbb R)$, J. Funct. Anal. 276 (1) (2019) 78-126. https://dx.doi.org/10.1016/j.jfa.2018.09.013
A. Kosyak, P. Moree, E. Sofos and B. Zhang, Cyclotomic polynomials with prescribed height and prime number theory, http://arxiv.org/abs/1910.01039, to appear in Mathematika, pp. 23.
Kosyak A.V. Regular, quasiregular and induced representations of infinite-dimensional groups, EMS (Europ. Math. Soc) Tracts in Mathematics 29, 587 p. 2018. https://doi.org/10.4171/181
Research papers:
Kosyak A.V. and Samoilenko Yu.S. On families of commuting self-adjoint operators, {\it Ukrain. Math. Journ.} 1979, v.31, no.5, p.555-558.
Kosyak A.V. Garding domain and entire vectors for inductive limits of Abelian locally-compact groups, {\it Ukrain. Math. Journ.} 1983, v.35, no. 4, p.427-434.
Kosyak A.V. Garding domain for representations of canonical commuting relations, {\it Ukrain. Math. Journ.} 1984, v.36, no.6, p.709-715.
Kosyak A.V. Extension of unitary representations of inductive limits of finite-dimensional Lie groups, {\it Rep. Math. Phys.} 1988, v.26, no.2, p.129-148.
Kosyak A.V. Irreducibility criterion for regular Gaussian representations of
group of finite upper-triangular matrices, {\it Funct. Anal. i Priloz.} 1990, v.24, issue 3, p.82-83.
Kosyak A.V. and Samoilenko Yu.S. Quasi-invariant measures on { \it Large} groups. {\it Selecta Math. Sov.} 1991, v.10, no.1, p.1-6 .
Kosyak A.V. Criteria for irreducibility and equivalence of regular Gaussian representations of group of finite upper-trianguler matrices of infinite order, {\it Selecta Math. Sov.} 1992, v.11, no.3, p.241-291.
Kosyak A.V. Irreducible regular Gaussian representations of the group of the interval and circle diffeomorphisms, {\it Journ. Funct. Anal.} 1994, v.125, p.493-547.
Kosyak A.V. and Zekri R. Type of von Neumann algebras generated by regular representations of infinite dimensional groups.{\it Vestnik Tambov Univ.} 1998, vol. 3, issue 1, 47-48.
Kosyak A.V. Measures on infinite-dimensional groups quasi-invariant with respect to inverse mapping and the commutant theorem, Analysis on infinite-dimensional Lie groups and algebras (Marseille, 1997),182-196, World Sci. Publishing, River Edge, NJ, 1998.
Kosyak A.V. and Zekri R. Anti-Wick symbols on infinite tensor product spaces.
{\it Methods of Funct. Anal. and Topology}. 1999, v.5, No 2, p.29-39.
Kosyak A.V. Inversion-quasi-invariant Gaussian measures on the group of
infinite-order upper-triangular matrices. {\it Funct. Anal. i Priloz. 2000,} v.34, issue 1, p.86-90.
Kosyak A.V. and Zekri R. Regular representations of infinite-dimensional groups and factors, I. {\it Methods of Funct. Anal. and Topology.} 2000, v.6, No 2, p. 50-59.
Kosyak A.V. Regular representations of the group of finite upper-triangular matrices, corresponding to product measures and criteria for their irreducibility. {\it Methods of Funct. Anal. and Topology.} 2000, v.6, No 4, p.43-56.
Kosyak A.V. Elementary representations of the group $B_0^{\Bbb N}$ I. {\it Methods of Funct. Anal. and Topology.} 2001, v.7, No 1, p.34-44.
Kosyak A.V. Irreducibility of the regular Gaussian representations of the group $B_0^{\mathbb Z}$. {\it Methods of Funct. Anal. and Topology.} 2001, v.7, No 2, p.42-51.
Kosyak A.V. and Zekri R. Regular representations of infinite-dimensional group $B_0^{\mathbb Z}$ and factors. {\it Methods of Funct. Anal. and Topology.} 2001, v.7, No 4, p.43 - 48 (co-author R.Zekri)
Kosyak A.V. Elementary representations of the group $B_0^{\Bbb Z}$. I. {\it Ukrain. Math. Journ.} 2002, v.54, No 2, p.205-215.
Kosyak A.V. Generalized Ismagilov conjecture for the group $B_0^{\Bbb N}$. I.{\it Methods of Funct. Anal. and Topology.} 2002, v.8, No 2, p.33-49.
Kosyak A.V. Generalized Ismagilov conjecture for the group $B_0^{\Bbb N}$. II.{\it Methods of Funct. Anal. and Topology.} 2002, v.8, No 3, p.27-45.
Kosyak A.V. and L\'eandre R. Regular Representations of the Central Extension of the Group of Diffeomorphisms of a Circle. {\it Doklady Mathematics.} 2002, v.66, No 1, p.75-77 . From {\it Doklady Akademii Nauk}, v.385, No 4, p.453-455
Kosyak A.V. Irreducibility criterion for quasiregular representations of the group of finite upper-trianguler matrices. {\it Funct. Anal. i Priloz.} 2003, v.37, issue 1, p.78-81.
Kosyak A.V. and Zekri R. Anti - Wick symbols for infinite products in K-homology, {\it K-theory.} 2003, v. 29 117-145.
Kosyak A.V. Quasi-invariant measures and irreducible representations of the inductive limit of special linear groups. {\it Functional Analysis and Its Applications}, Vol. 38, No 1, pp.67-68, 2004.
Kosyak A. and Albeverio S. Quasi-regular representations of the infinite-dimensional Borel group. {\it Journ. Funct. Anal.} v. 218, issue 2 (2005) 445-474.
Kosyak A.V. and Nizhnik L.P. Generalized translation operators and hipergroups constructed from self-adjoint operators, {\it Ukrain. Math. Journ.} 2005, v.57, no.5, p.659-669.
Kosyak A. and Albeverio S. Group action, quasi-invariant measures and quasiregular representations of the infinite-dimensional nilpotent group, {\it Contemporary Mathematics of AMS}. 2005, v.385, 259-280. 364 p.
Kosyak A. and Albeverio S. Quasiregular representations of the infinite-dimensional nilpotent group, {\it J. Funct. Anal.} 236 (2006) 634-681.
A. V. Kosyak, A. Yu. Khrennikov, V. M. Shelkovich, Pseudodifferential operators on adele rings and wavelet bases. Doklady Mathematics, 85, 358–362 (2012). https://doi.org/10.1134/S1064562412030167
A. V. Kosyak, A. Yu. Khrennikov, V. M. Shelkovich, Wavelet bases on adele rings, Doklady Mathematics, 85, 75–79 (2012). https://doi.org/10.1134/S1064562412010267
A. Yu. Khrennikov, A.V. Kosyak, V.M. Shelkovich Wavelet analysis on adeles and pseudo-differential operators, Journal of Fourier Analysis and Applications 18 (6), (2012) 1215-1264. https://doi.org/10.1007/s00041-012-9233-6
A.V. Kosyak, Induced representations of infinite-dimensional groups, I. J. Funct. Anal. 266 (6) (2014) 3395-3434. https://doi.org/10.1016/j.jfa.2014.01.008
A.V. Kosyak, Criteria of irreducibility of the Koopman representations for the group ${\rm GL}_0(2\infty,\mathbb R)$, J. Funct. Anal. 276 (1) (2019) 78-126. https://dx.doi.org/10.1016/j.jfa.2018.09.013
A. Kosyak, P. Moree, E. Sofos and B. Zhang, Cyclotomic polynomials with prescribed height and prime number theory, http://arxiv.org/abs/1910.01039, to appear in Mathematika, pp. 23.