01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
25.12.1976
E-mail:
,
Keywords:
eigenvalues,
spectrum.
UDC:
517.984
Subject:
Spectral properties of the block operator matrices.
Main publications:
M. I. Muminov, T. H. Rasulov, “The Faddeev Equation and Essential Spectrum of a Hamiltonian in Fock Space”, Methods of Functional Analysis and Topology, 17:1 (2011), 47–57
T. H. Rasulov, “Investigations of the Essential Spectrum of a Hamiltonian in Fock Space”, Applied Mathematics & Information Sciences, 4:3 (2010), 395–412
T. H. Rasulov, M. I. Muminov, M. Hasanov, “On the Spectrum of a Model Operator in Fock Space”, Methods of Functional Analysis and Topology, 15:4 (2009), 369–383
S. Albeverio, S. N. Lakaev, T. H. Rasulov, “On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum asymptotics”, Journal of Statistical Physics, 127:2 (2007), 191–220
S. Albeverio, S. N. Lakaev, T. H. Rasulov, “The Efimov Effect for a Model Operator Associated to a System of three non Conserved Number of Particles”, Methods of Functional Analysis and Topology, 13:1 (2007), 1–16
T. H. Rasulov, A. M. Khalkhuzhaev, M. A. Pardabaev, Kh. G. Khayitova, “Expansions of eigenvalues of a discrete bilaplacian with two-dimensional perturbation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 10, 77–89
2.
T. Kh. Rasulov, D. E. Ismoilova, “Spectral relations for a matrix model in fermionic Fock space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 3, 91–96
3.
M. I. Muminov, I. N. Bozorov, T. Kh. Rasulov, “On the number of components of the essential spectrum of one $2\times2$ operator matrix”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 2, 85–90
2023
4.
T. H. Rasulov, E. B. Dilmurodov, “Main properties of the Faddeev equation for $2 \times 2$ operator matrices”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 12, 53–58
5.
M. Rehman, T. Rasulov, B. Aminov, “Non-negative matrices and their structured singular values”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 10, 36–45
6.
J. I. Abdullaev, A. M. Khalkhuzhaev, T. H. Rasulov, “Existence condition of an eigenvalue of the three particle Schrödinger operator on a lattice”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 9, 3–19
B. I. Bahronov, T. H. Rasulov, M. Rehman, “Conditions for the existence of eigenvalues of a three-particle lattice model Hamiltonian”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 7, 3–12
Tulkin Rasulov, Elyor Dilmurodov, “The first Schur complement for a lattice spin-boson model with at most two photons”, Nanosystems: Physics, Chemistry, Mathematics, 14:3 (2023), 304–311
9.
Tulkin H. Rasulov, Bekzod I. Bahronov, “Existence of the eigenvalues of a tensor sum of the Friedrichs models with rank 2 perturbation”, Nanosystems: Physics, Chemistry, Mathematics, 14:2 (2023), 151–157
10.
T. H. Rasulov, H. M. Latipov, “Description of the spectrum of one fourth-order operator matrix”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 27:3 (2023), 427–445
2020
11.
T. H. Rasulov, E. B. Dilmurodov, “Analysis of the spectrum of a $2\times 2$ operator matrix. Discrete spectrum asymptotics”, Nanosystems: Physics, Chemistry, Mathematics, 11:2 (2020), 138–144
T. H. Rasulov, E. B. Dilmurodov, “Infinite number of eigenvalues of $2\times 2$ operator matrices: Asymptotic discrete spectrum”, TMF, 205:3 (2020), 368–390; Theoret. and Math. Phys., 205:3 (2020), 1564–1584
T. H. Rasulov, E. B. Dilmurodov, “Threshold analysis for a family of $2\times2$ operator matrices”, Nanosystems: Physics, Chemistry, Mathematics, 10:6 (2019), 616–622
T. H. Rasulov, N. A. Tosheva, “Analytic description of the essential spectrum of a family of $3\times 3$ operator matrices”, Nanosystems: Physics, Chemistry, Mathematics, 10:5 (2019), 511–519
2016
15.
T. H. Rasulov, “Branches of the essential spectrum of the lattice spin-boson model with at most two photons”, TMF, 186:2 (2016), 293–310; Theoret. and Math. Phys., 186:2 (2016), 251–267
Mukhiddin I. Muminov, Tulkin H. Rasulov, “Universality of the discrete spectrum asymptotics of the three-particle Schrödinger operator on a lattice”, Nanosystems: Physics, Chemistry, Mathematics, 6:2 (2015), 280–293
T. Kh. Rasulov, Z. D. Rasulova, “On the spectrum of a three-particle model operator on a lattice with non-local potentials”, Sib. Èlektron. Mat. Izv., 12 (2015), 168–184
18.
M. É. Muminov, T. Kh. Rasulov, “An eigenvalue multiplicity formula for the Schur complement of a $3\times3$ block operator matrix”, Sibirsk. Mat. Zh., 56:4 (2015), 878–895; Siberian Math. J., 56:4 (2015), 699–713
M. I. Muminov, T. H. Rasulov, “Infiniteness of the number of eigenvalues embedded in the essential spectrum of a $2\times2$ operator matrix”, Eurasian Math. J., 5:2 (2014), 60–77
T. Kh. Rasulov, R. T. Mukhitdinov, “The finiteness of the discrete spectrum of a model operator associated with a system of three particles on a lattice”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 1, 61–70; Russian Math. (Iz. VUZ), 58:1 (2014), 52–59
M. I. Muminov, T. H. Rasulov, “On the number of eigenvalues of the family of operator matrices”, Nanosystems: Physics, Chemistry, Mathematics, 5:5 (2014), 619–625
22.
T. H. Rasulov, Z. D. Rasulova, “Essential and discrete spectrum of a three-particle lattice Hamiltonian with non-local potentials”, Nanosystems: Physics, Chemistry, Mathematics, 5:3 (2014), 327–342
23.
T. H. Rasulov, I. O. Umarova, “Spectrum and resolvent of a block operator matrix”, Sib. Èlektron. Mat. Izv., 11 (2014), 334–344
24.
T. H. Rasulov, E. B. Dilmurodov, “Investigations of the Numerical Range of a Operator Matrix”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(35) (2014), 50–63
T. H. Rasulov, “Structure of the essential spectrum of a model operator associated to a system of three particles on a lattice”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(27) (2012), 34–43
2011
26.
T. Kh. Rasulov, “On the number of eigenvalues of a matrix operator”, Sibirsk. Mat. Zh., 52:2 (2011), 400–415; Siberian Math. J., 52:2 (2011), 316–328
T. H. Rasulov, “Essential spectrum of a model operator associated with a three-particle system on a lattice”, TMF, 166:1 (2011), 95–109; Theoret. and Math. Phys., 166:1 (2011), 81–93
T. Kh. Rasulov, “On the essential spectrum of a model operator associated with the system of three particles on a lattice”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(24) (2011), 42–51
T. Kh. Rasulov, A. A. Rakhmonov, “The Faddeev equation and location of the essential spectrum of a three-particle model operator”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(23) (2011), 170–180
2010
31.
T. H. Rasulov, “Study of the essential spectrum of a matrix operator”, TMF, 164:1 (2010), 62–77; Theoret. and Math. Phys., 164:1 (2010), 883–895
T. H. Rasulov, “Asymptotics of the discrete spectrum of a model operator associated with a system of three particles on a lattice”, TMF, 163:1 (2010), 34–44; Theoret. and Math. Phys., 163:1 (2010), 429–437
T. H. Rasulov, “Investigation of the spectrum of a model operator in a Fock space”, TMF, 161:2 (2009), 164–175; Theoret. and Math. Phys., 161:2 (2009), 1460–1470
T. H. Rasulov, “The Faddeev equation and the location of the essential spectrum of a model operator for several particles”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 12, 59–69; Russian Math. (Iz. VUZ), 52:12 (2008), 50–59
T. H. Rasulov, “On the Structure of the Essential Spectrum of a Model Many-Body Hamiltonian”, Mat. Zametki, 83:1 (2008), 86–94; Math. Notes, 83:1 (2008), 80–87
S. N. Lakaev, T. H. Rasulov, “Efimov's Effect in a Model of Perturbation Theory of the Essential Spectrum”, Funktsional. Anal. i Prilozhen., 37:1 (2003), 81–84; Funct. Anal. Appl., 37:1 (2003), 69–71
S. N. Lakaev, T. H. Rasulov, “A Model in the Theory of Perturbations of the Essential Spectrum of Multiparticle Operators”, Mat. Zametki, 73:4 (2003), 556–564; Math. Notes, 73:4 (2003), 521–528
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