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Danilov, Leonid Ivanovich

Statistics Math-Net.Ru
Total publications: 45
Scientific articles: 45

Number of views:
This page:689
Abstract pages:8243
Full texts:3053
References:1122
Senior Researcher
Candidate of physico-mathematical sciences (1991)
Speciality: 01.01.03 (Mathematical physics)
Birth date: 10.02.1957
E-mail: ,
Keywords: periodic Schrodinger and Dirac operators; almost periodic functions; selectors of multivalued maps.

Subject:

The absolute continuity of the spectra of periodic Schrodinger and Dirac operators is investigated under various conditions on electric $V$ and magnetic $A$ potentials. A number of papers were devoted to almost periodic measure-valued functions and almost periodic selectors of multivalued maps.

Biography

Graduated from Faculty of General and Applied Physics of MIPT (Moscow Institute of Physics and Technology) in 1981. Ph.D. thesis was defended in 1990.

   
Main publications:
  • Danilov L. I. Otsenki yadra Puassona dlya trubchatoi oblasti nad ostrym konusom // Doklady AN SSSR. 1991, 316 (4), 805–807.
  • Danilov L. I. Meroznachnye pochti periodicheskie funktsii i pochti periodicheskie secheniya mnogoznachnykh otobrazhenii // Matem. sbornik. 1997, 188 (10), 3–24.
  • Danilov L. I. O pochti periodicheskikh meroznachnykh funktsiyakh // Matem. sbornik. 2000, 191 (12), 27–50.
  • Danilov L. I. Ob otsutstvii sobstvennykh znachenii v spektre obobschennogo dvumernogo periodicheskogo operatora Diraka // Algebra i analiz. 2005, 17 (3), 47–80.
  • Danilov L. I. On absolute continuity of the spectrum of three- and four-dimensional periodic Schrodinger operators // J. Phys. A: Math. Theor. 2010, 43, 215201.

http://www.mathnet.ru/eng/person8547
List of publications on Google Scholar
https://zbmath.org/authors/?q=ai:danilov.l-i
https://mathscinet.ams.org/mathscinet/MRAuthorID/219362
ISTINA http://istina.msu.ru/workers/57998667
http://www.researcherid.com/rid/C-7076-2008

Publications in Math-Net.Ru
2020
1. L. I. Danilov, “On the spectrum of a Landau Hamiltonian with a periodic electric potential $V\in L^p_{\mathrm {loc}}(\mathbb{R}^2)$, $p>1$”, Izv. IMI UdGU, 55 (2020),  42–59  mathnet  elib
2. L. I. Danilov, “Spectrum of the Landau Hamiltonian with a periodic electric potential”, TMF, 202:1 (2020),  47–65  mathnet  mathscinet  elib; Theoret. and Math. Phys., 202:1 (2020), 41–57  isi  scopus
2019
3. L. I. Danilov, “On the spectrum of a relativistic Landau Hamiltonian with a periodic electric potential”, Izv. IMI UdGU, 54 (2019),  3–26  mathnet  elib
2018
4. L. I. Danilov, “On the spectrum of a two-dimensional schrödinger operator with a homogeneous magnetic field and a periodic electric potential”, Izv. IMI UdGU, 51 (2018),  3–41  mathnet  elib
5. L. I. Danilov, “Shift dynamical systems and measurable selectors of multivalued maps”, Mat. Sb., 209:11 (2018),  69–102  mathnet  mathscinet  elib; Sb. Math., 209:11 (2018), 1611–1643  isi  scopus
2016
6. L. I. Danilov, “On the spectrum of a periodic magnetic Dirac operator”, Izv. IMI UdGU, 2016, 2(48),  3–21  mathnet  elib
2015
7. L. I. Danilov, “Recurrent and almost automorphic selections of multivalued mappings”, Izv. IMI UdGU, 2015, 2(46),  45–52  mathnet  elib
2014
8. L. I. Danilov, “Recurrent and almost recurrent multivalued maps and their selections. III”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, 4,  25–52  mathnet
9. L. I. Danilov, “On the spectrum of a two-dimensional generalized periodic Schrödinger operator. II”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, 2,  3–28  mathnet
2013
10. L. I. Danilov, “On the spectrum of a two-dimensional generalized periodic Schrödinger operator”, Izv. IMI UdGU, 2013, 1(41),  78–95  mathnet
11. L. I. Danilov, “The uniform approximation of recurrent functions and almost recurrent functions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, 4,  36–54  mathnet
2012
12. L. I. Danilov, “Recurrent and almost recurrent multivalued maps and their selections. II”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, 4,  3–21  mathnet
13. L. I. Danilov, “On the spectrum of a periodic Schrödinger operator with potential in the Morrey space”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, 3,  25–47  mathnet
2011
14. L. I. Danilov, “Recurrent and almost recurrent multivalued maps and their selections”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, 2,  19–51  mathnet  elib
2009
15. L. I. Danilov, “On a class of Weyl almost periodic selections of multivalued maps”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, 1,  24–45  mathnet  elib
2008
16. L. I. Danilov, “On almost periodic sections of multivalued maps”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, 2,  34–41  mathnet  elib
17. L. I. Danilov, “On Besicovitch almost periodic selections of multivalued maps”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, 1,  97–120  mathnet  elib
18. L. I. Danilov, “Absolute continuity of the spectrum of multidimensional periodic magnetic Dirac operator”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, 1,  61–96  mathnet
2006
19. L. I. Danilov, “Weyl almost periodic selections of multivalued maps”, Izv. IMI UdGU, 2006, 3(37),  27–28  mathnet
20. L. I. Danilov, “On absolute continuity of the spectrum of three-dimensional periodic Dirac operator”, Izv. IMI UdGU, 2006, 1(35),  49–76  mathnet
21. L. I. Danilov, “On uniform approximation of Weyl and Besicovitch almost periodic functions”, Izv. IMI UdGU, 2006, 1(35),  33–48  mathnet
22. L. I. Danilov, “Weyl almost periodic selections of supports of measure-valued functions”, Sib. Èlektron. Mat. Izv., 3 (2006),  384–392  mathnet  mathscinet  zmath
2005
23. L. I. Danilov, “The absence of eigenvalues in the spectrum of ageneralized two-dimensional periodic Dirac operator”, Algebra i Analiz, 17:3 (2005),  47–80  mathnet  mathscinet  zmath; St. Petersburg Math. J., 17:3 (2006), 409–433
24. L. I. Danilov, “On Weyl almost periodic measure-valued functions”, Izv. IMI UdGU, 2005, 1(31),  79–98  mathnet
2004
25. L. I. Danilov, “On absence of eigenvalues in the spectra of two-dimensional periodic Dirac and Schrödinger operators”, Izv. IMI UdGU, 2004, 1(29),  49–84  mathnet
26. L. I. Danilov, “Uniform approximation of Stepanov almost periodic functions”, Izv. IMI UdGU, 2004, 1(29),  33–48  mathnet
2003
27. L. I. Danilov, “Absolute Continuity of the Spectrum of a Periodic Schrödinger Operator”, Mat. Zametki, 73:1 (2003),  49–62  mathnet  mathscinet  zmath; Math. Notes, 73:1 (2003), 46–57  isi
28. L. I. Danilov, “The Spectrum of the Two-Dimensional Periodic Schrödinger Operator”, TMF, 134:3 (2003),  447–459  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 134:3 (2003), 392–403  isi
2002
29. L. I. Danilov, “On the spectra of two-dimensional periodic Schrödinger and Dirac operators”, Izv. IMI UdGU, 2002, 3(26),  3–98  mathnet
2000
30. L. I. Danilov, “Absolute continuity of the spectrum of a periodic Dirac operator”, Differ. Uravn., 36:2 (2000),  233–240  mathnet  mathscinet; Differ. Equ., 36:2 (2000), 262–271
31. L. I. Danilov, “On almost periodic multivalued maps”, Mat. Zametki, 68:1 (2000),  82–90  mathnet  mathscinet  zmath  elib; Math. Notes, 68:1 (2000), 71–77  isi
32. L. I. Danilov, “Almost periodic measure-valued functions”, Mat. Sb., 191:12 (2000),  27–50  mathnet  mathscinet  zmath  elib; Sb. Math., 191:12 (2000), 1773–1796  isi  scopus
33. L. I. Danilov, “Spectrum of the periodic Dirac operator”, TMF, 124:1 (2000),  3–17  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 124:1 (2000), 859–871  isi
1999
34. L. I. Danilov, “On the spectrum of the two-dimensional periodic Dirac operator”, TMF, 118:1 (1999),  3–14  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 118:1 (1999), 1–11  isi
1998
35. L. I. Danilov, “On the uniform approximation of a function that is almost periodic in the sense of Stepanov”, Izv. Vyssh. Uchebn. Zaved. Mat., 1998, 5,  10–18  mathnet  mathscinet  elib; Russian Math. (Iz. VUZ), 42:5 (1998), 8–16
1997
36. L. I. Danilov, “Measure-valued almost periodic functions”, Mat. Zametki, 61:1 (1997),  57–68  mathnet  mathscinet  zmath; Math. Notes, 61:1 (1997), 48–57
37. L. I. Danilov, “Measure-valued almost periodic functions and almost periodic selections of multivalued maps”, Mat. Sb., 188:10 (1997),  3–24  mathnet  mathscinet  zmath; Sb. Math., 188:10 (1997), 1417–1438  isi  scopus
1995
38. L. I. Danilov, “Resolvent estimates and the spectrum of the Dirac operator with periodical potential”, TMF, 103:1 (1995),  3–22  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 103:1 (1995), 349–365  isi
1994
39. L. I. Danilov, A. G. Ivanov, “On a pointwise maximum theorem in the almost periodic case”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, 6,  50–59  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 38:6 (1994), 48–57
1991
40. L. I. Danilov, “Estimates for the Poisson kernel for a tube domain over an acute cone”, Dokl. Akad. Nauk SSSR, 316:4 (1991),  805–807  mathnet  mathscinet  zmath; Dokl. Math., 43:1 (1991), 181–183
41. L. I. Danilov, A. G. Ivanov, “A comparison theorem on the uniform oscillation of a linear equation”, Differ. Uravn., 27:9 (1991),  1636–1637  mathnet  mathscinet  zmath
42. L. I. Danilov, A. G. Ivanov, “Effective sufficient conditions for the uniform oscillation of a linear differential equation”, Mat. Zametki, 49:3 (1991),  28–34  mathnet  mathscinet  zmath; Math. Notes, 49:3 (1991), 248–252  isi
1990
43. L. I. Danilov, A. G. Ivanov, “Effective sufficient conditions for uniform local controllability”, Differ. Uravn., 26:4 (1990),  563–572  mathnet  mathscinet  zmath; Differ. Equ., 26:4 (1990), 406–413
44. L. I. Danilov, “Spectrum of the Dirac operator in $\mathbb R^n$ with periodic potential”, TMF, 85:1 (1990),  41–53  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 85:1 (1990), 1039–1048  isi
1985
45. L. I. Danilov, “Regularity of an acute open cone in $\mathbf{R}^n$”, Sibirsk. Mat. Zh., 26:2 (1985),  198–201  mathnet  mathscinet  zmath

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