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Danilov, Leonid Ivanovich

Statistics Math-Net.Ru
Total publications: 43
Scientific articles: 43

Number of views:
This page:649
Abstract pages:7252
Full texts:2751
References:1095
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
http://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, “Spectrum of the Landau Hamiltonian with a periodic electric potential”, TMF, 202:1 (2020),  47–65  mathnet  elib; Theoret. and Math. Phys., 202:1 (2020), 41–57  isi  scopus
2019
2. L. I. Danilov, “On the spectrum of a relativistic Landau Hamiltonian with a periodic electric potential”, Izv. IMI UdGU, 54 (2019),  3–26  mathnet
2018
3. 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
4. L. I. Danilov, “Shift dynamical systems and measurable selectors of multivalued maps”, Mat. Sb., 209:11 (2018),  69–102  mathnet  elib; Sb. Math., 209:11 (2018), 1611–1643  isi  scopus
2016
5. L. I. Danilov, “On the spectrum of a periodic magnetic Dirac operator”, Izv. IMI UdGU, 2016, 2(48),  3–21  mathnet  elib
2015
6. L. I. Danilov, “Recurrent and almost automorphic selections of multivalued mappings”, Izv. IMI UdGU, 2015, 2(46),  45–52  mathnet  elib
2014
7. 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
8. 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
9. L. I. Danilov, “On the spectrum of a two-dimensional generalized periodic Schrödinger operator”, Izv. IMI UdGU, 2013, 1(41),  78–95  mathnet
10. 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
11. 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
12. 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
13. 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
14. 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
15. L. I. Danilov, “On almost periodic sections of multivalued maps”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, 2,  34–41  mathnet  elib
16. L. I. Danilov, “On Besicovitch almost periodic selections of multivalued maps”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, 1,  97–120  mathnet  elib
17. 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
18. L. I. Danilov, “Weyl almost periodic selections of multivalued maps”, Izv. IMI UdGU, 2006, 3(37),  27–28  mathnet
19. L. I. Danilov, “On absolute continuity of the spectrum of three-dimensional periodic Dirac operator”, Izv. IMI UdGU, 2006, 1(35),  49–76  mathnet
20. L. I. Danilov, “On uniform approximation of Weyl and Besicovitch almost periodic functions”, Izv. IMI UdGU, 2006, 1(35),  33–48  mathnet
21. 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
22. 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
23. L. I. Danilov, “On Weyl almost periodic measure-valued functions”, Izv. IMI UdGU, 2005, 1(31),  79–98  mathnet
2004
24. 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
25. L. I. Danilov, “Uniform approximation of Stepanov almost periodic functions”, Izv. IMI UdGU, 2004, 1(29),  33–48  mathnet
2003
26. 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
27. 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
28. L. I. Danilov, “On the spectra of two-dimensional periodic Schrödinger and Dirac operators”, Izv. IMI UdGU, 2002, 3(26),  3–98  mathnet
2000
29. 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
30. 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
31. 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
32. 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
33. 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
34. 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
35. 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
36. 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
37. 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
38. 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
39. 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
40. 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
41. 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
42. 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
43. 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

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