Spectral properties of the many-body Hamiltonians on lattice. Fridrichs Model.
Main publications:
Mukhiddin I. Muminov and Tulkin H. Rasulov. The Faddeev Equation and Essential Spectrum of a Hamiltonian in Fock Space. Refereed ICTP Preprint, IC/2008/027.
Tulkin H. Rasulov and Mukhiddin I. Muminov. The Essential Spectrum of a Model Operator in Fock Space. Refereed ICTP Preprint, IC/2008/013.
Tulkin H. Rasulov, Mukhiddin I. Muminov and Mahir Hasanov. On the Spectrum of a Model Operator in Fock Space. ArXiv: math-ph 0805.1284v1, 2008.
M. I. Muminov. On the number of eigenvalues of the generalized
Friedrichs model. Uzbek Mathematical Journal (2007), No. 4,
00–11 (Russian).
Zh. I. Abdullaev, M. I. Muminov. On spectrum of sub-hamiltonians of n-particles on lattice. Uzbek Mathematical Journal (2006), No. 1, 3–8.
Zh. I. Abdullaev, M. I. Muminov. On the essential spectrum four particle Schrödinger Operator interacting via zero-range attractive potentials. DAN RUz, 2002, No. 3, 12–15 (Russian).
S. N. Lakaev, M. I. Muminov. On the essential spectrum of the non self-adjoint generalized Friedrichs model. Doklady Res. Uzb., 1997, No. 4, 8–10(Russian).
M. I. Muminov. On spectrum of the non self-adjoint generalized Friedrichs model. Uzbek. math. journal, 1997, No. 1, 48–58 (Russian).
S. N. Lakaev, M. E. Muminov. On spectrum of the non self-adjoint generalized Friedrichs model. DAN UzSSR, 1995, No. 7–8, p. 7–11 (Russian).
M. I. Muminov, U. R. Shadiev, “On the existence of an eigenvalue of the generalized Friedrichs model”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 4, 31–38
2.
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
3.
Mukhiddin I. Muminov, Abdimajid M. Hurramov, Islom N. Bozorov, “On eigenvalues and virtual levels of a two-particle Hamiltonian on a $d$-dimensional lattice”, Nanosystems: Physics, Chemistry, Mathematics, 14:3 (2023), 295–303
Mukhiddin I. Muminov, Zarifjon Kh. Ochilov, “An inversion formula for the weighted Radon transform along family of cones”, Nanosystems: Physics, Chemistry, Mathematics, 14:1 (2023), 22–27
Mukhiddin I. Muminov, Tirkash A. Radjabov, “On existence conditions for periodic solutions to a differential equation with constant argument”, Nanosystems: Physics, Chemistry, Mathematics, 13:5 (2022), 491–497
6.
M. I. Muminov, A. M. Khurramov, I. N. Bozorov, “Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice”, Nanosystems: Physics, Chemistry, Mathematics, 13:3 (2022), 237–244
M. I. Muminov, C. Lokman, “Finiteness of discrete spectrum of the two-particle Schrödinger operator on diamond lattices”, Nanosystems: Physics, Chemistry, Mathematics, 8:3 (2017), 310–316
2016
8.
M. E. Muminov, E. M. Shermatova, “On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 1, 27–35; Russian Math. (Iz. VUZ), 60:1 (2016), 22–29
9.
M. I. Muminov, A. M. Khurramov, “Spectral properties of a two-particle hamiltonian on a $d$-dimensional lattice”, Nanosystems: Physics, Chemistry, Mathematics, 7:5 (2016), 880–887
2015
10.
M. I. Muminov, A. M. Khurramov, “On compact distribution of two-particle Schrödinger operator on a lattice”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 6, 24–30; Russian Math. (Iz. VUZ), 59:6 (2015), 18–22
11.
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
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, N. M. Aliev, “Discrete spectrum of a noncompact perturbation of a three-particle Schrödinger operator on a lattice”, TMF, 182:3 (2015), 435–452; Theoret. and Math. Phys., 182:3 (2015), 381–396
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
N. M. Aliev, M. E. Muminov, “On the spectrum of the three-particle Hamiltonian on a unidimensional lattice”, Mat. Tr., 17:2 (2014), 3–22; Siberian Adv. Math., 25:3 (2015), 155–168
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
17.
M. I. Muminov, A. M. Hurramov, “Multiplicity of virtual levels at the lower edge of the continuous spectrum of a two-particle Hamiltonian on a lattice”, TMF, 180:3 (2014), 329–341; Theoret. and Math. Phys., 180:3 (2014), 1040–1050
M. E. Muminov, A. M. Khurramov, “Spectral properties of two particle Hamiltonian on one-dimensional lattice”, Ufimsk. Mat. Zh., 6:4 (2014), 102–110; Ufa Math. J., 6:4 (2014), 99–107
M. I. Muminov, A. M. Hurramov, “Spectral properties of a two-particle Hamiltonian on a lattice”, TMF, 177:3 (2013), 482–496; Theoret. and Math. Phys., 177:3 (2013), 1693–1705
M. É. Muminov, N. M. Aliev, “Spectrum of the three-particle Schrödinger operator on a one-dimensional lattice”, TMF, 171:3 (2012), 387–403; Theoret. and Math. Phys., 171:3 (2012), 754–768
M. E. Muminov, U. R. Shodiev, “Spectral properties of a Hamiltonian of a four-particle system on a lattice”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 12, 32–43; Russian Math. (Iz. VUZ), 54:12 (2010), 27–37
22.
M. I. Muminov, U. R. Shodiev, “On the essential spectrum of a four-particle Schrödinger operator on a lattice”, Mat. Tr., 13:1 (2010), 169–185; Siberian Adv. Math., 21:4 (2011), 292–303
23.
M. I. Muminov, “Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice”, TMF, 164:1 (2010), 46–61; Theoret. and Math. Phys., 164:1 (2010), 869–882
M. I. Muminov, “The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrödinger operator on a lattice”, TMF, 159:2 (2009), 299–317; Theoret. and Math. Phys., 159:2 (2009), 667–683
M. I. Muminov, “Finiteness of the discrete spectrum of the Schrödinger operator of
three particles on a lattice”, TMF, 154:2 (2008), 363–371; Theoret. and Math. Phys., 154:2 (2008), 311–318
M. I. Muminov, “Positivity of the two-particle Hamiltonian on a lattice”, TMF, 153:3 (2007), 381–387; Theoret. and Math. Phys., 153:3 (2007), 1671–1676
M. I. Muminov, “A Hunziker–van Winter–Zhislin theorem for a four-particle lattice Schrödinger operator”, TMF, 148:3 (2006), 428–443; Theoret. and Math. Phys., 148:3 (2006), 1236–1250
G. R. Yodgorov, M. I. Muminov, “Spectrum of a Model Operator in the Perturbation Theory of the Essential Spectrum”, TMF, 144:3 (2005), 544–554; Theoret. and Math. Phys., 144:3 (2005), 1344–1352
S. N. Lakaev, M. I. Muminov, “Essential and Discrete Spectra of the Three-Particle Schrödinger Operator on a Lattice”, TMF, 135:3 (2003), 478–503; Theoret. and Math. Phys., 135:3 (2003), 849–871
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