*The asymptotic distribution of eigenvalues of partial differential
operators*, American Mathematical Society,
1997 (hardcover), 1998 (softcover),
series Translations of Mathematical Monographs, vol. 155.
Jointly with Yu.Safarov.
The book can be ordered from the
AMS Bookstore.
Here is the list of
typos.

1. *On the zeros of determinants of Wronski type*, Transactions of
the 20 Scientific Conference (1974) of the Moscow Institute of Physics and
Technology, series *Aerophysics and applied mathematics*, part **2**,
p. 116-121 (in Russian).

2. *On the dependence of eigenvalues on the length of the segment
under the clamping condition at one of the ends*, Transactions of the
21 Scientific Conference (1975) of the Moscow Institute of Physics and
Technology, series *Aerophysics and applied mathematics*, p. 170-174
(in Russian).

3. *On the zeros of the bending deflection function in the theory of
free vibrations of shells of revolution*, Soviet Mathematics Doklady **
18**, p. 1470-1473.

4. *On the eigenfunctions of a thin elastic shell of revolution under
the condition of internal resonance*, Transactions of the 23 Scientific
Conference (1977) of the Moscow Institute of Physics and
Technology, series
*Aerophysics and applied mathematics*, p. 133-136 (in Russian).

5. *A formula for the frequency distribution function of a shell of
revolution immersed in a liquid*, Soviet Physics Doklady **24**, p.
720-722.

6. *Vibrations of thin elastic shells interacting with a liquid*,
Uspekhi Mat. Nauk **35**, no. 2, p. 255-256 (in Russian). Jointly with
A.G.Aslanyan and V.B.Lidskii.

7. *Frequencies of free vibrations of a shell interacting with a
liquid*, Transactions of the 12 USSR Conference on the Theory of
Shells and Plates (Yerevan, 1980), vol. **2**, p. 86-92; Yerevan, publishing
house of the
Yerevan State University (in Russian). Jointly with A.G.Aslanyan and
V.B.Lidskii.

8. *Asymptotics of the distribution function of the spectrum of
pseudodifferential operators with parameters*, Functional Analysis and
its Applications **14**, p. 217-219.

9. *The distribution of eigenfrequencies of a thin elastic shell
interacting with a liquid*, Uspekhi Mat. Nauk **36**, no. 4, p. 216 (in
Russian). Jointly with A.G.Aslanyan and V.B.Lidskii.

10. *Frequencies of free vibrations of a thin shell interacting with
a liquid*, Functional Analysis and its Applications **15**, p. 157-164.
Jointly with A.G.Aslanyan and V.B.Lidskii.

11. *Asymptotic estimates of complex vibration frequencies of a shell
in a liquid*, preprint no. 186 of the Institute for
Problems in Mechanics of the USSR Academy of Sciences, 68 p. (in
Russian). Jointly with I.V.Simonov.

12. *Free vibrations of a shell interacting with a liquid*,
Transactions of the 2 USSR Symposium on the Physics of
Acoustohydrodynamic Phenomena and Optoacoustics (Suzdal, 1979), p.
264-266; Moscow, *Nauka* publishing house (in Russian). Jointly with
A.G.Aslanyan and V.B.Lidskii.

13. *Vibrations of thin elastic shells contacting liquid*, Uspekhi
Mat. Nauk **37**, no. 5, p. 224-225 (in Russian). Jointly with
V.B.Lidskii.

14.*Vibrations and radiation of a shell of revolution acted upon by
an annular load*, Mechanics of Solids **18**, no. 4, p. 183-191.
Jointly with A.L.Gol'denveizer.

15. *Binomial asymptotics of the spectrum of a boundary value
problem*, Functional Analysis and its Applications **17**, p. 309-311.

16. *Asymptotic analysis of vibrations of stiffened shells of
revolution contacting liquid*, Transactions of the 13 USSR
Conference on the Theory of Plates and Shells (Tallinn, 1983), vol. **1**, p.
169-174; Tallinn, publishing house of the Tallinn Polytechnic Institute
(in Russian).

17. *Two-term asymptotics of the spectrum of a boundary value problem
under an interior reflection of general type*, Uspekhi Mat. Nauk **
39**, no. 4, p. 131 (in Russian).

18. *Two-term asymptotics of the spectrum of a boundary value problem
under an interior reflection of general form*, Functional Analysis and
its Applications **18**, p. 267-277.

19. *A refinement of the Courant asymptotic formula for the
frequency distribution function of a plate*, Transactions of the
USSR Seminar on Theoretical and Numerical Methods for Plates and
Shells (Tbilisi, 1984), vol. **2**, p. 90-96; Tbilisi, publishing house
of the Tbilisi State University (in Russian).

20. *Asymptotics of the spectrum of pseudodifferential operators
with small parameters*, Math. USSR Sbornik **49**, no. 1, p.
61-72.

21. *Two-term asymptotics of the spectrum of a boundary value
problem with a piecewise smooth boundary*, Uspekhi Mat. Nauk **40**,
no. 5, p. 233 (in Russian).

22. *Forced vibrations of a thin elastic shell interacting with a
liquid*, in Mathematical Methods of the Mechanics of Solids
(series *Strength and viscoelastoplasticity*), p. 30-36; Moscow,
*Nauka* publishing house (in Russian). Jointly with V.B.Lidskii.

23. *Asymptotics of the spectrum of a differential operator on a
surface of revolution*, Izvestia of the Azerbaijani Academy of
Sciences, series *Physical-technical and mathematical sciences*,
**7**, no. 6, p. 23-28 (in Russian). Jointly with L.G.Khalilova.

24. *On the spectrum of the shell theory operator and the problem
*, in 11 USSR School on Operator Theory in
Functional Spaces (Chelyabinsk, 1986), part **2**, p. 22; Chelyabinsk,
publishing house of the Chelyabinsk Polytechnic Institute (in
Russian).

25. *Two-term asymptotics of the spectrum of a boundary value
problem in the case of a piecewise smooth boundary*, Soviet Mathematics
Doklady **33**, no. 1, p. 227-230.

26. *Forced vibrations of a thin
elastic shell interacting with a liquid*, Uspekhi Mat. Nauk **41**,
no. 4, p. 157-158 (in Russian). Jointly with V.B.Lidskii.

27. *Quasiresonances in the problem of forced vibrations of a thin
elastic shell interacting with a liquid*, Functional Analysis and its
Applications **20**, p. 267-276. Jointly with V.B.Lidskii.

28. *Asymptotics of the spectrum of a boundary value problem*,
Transactions of the Moscow Mathematical Society, p. 173-245.

29. *Hamiltonian systems with reflection*, Uspekhi Mat. Nauk **42**,
no. 4, p. 139-140 (in Russian).

30. *Vibrations of a shell filled with a viscous compressible liquid*,
Transactions of the 14 USSR Conference on the Theory of Plates and
Shells (Kutaisi, 1987), vol. **1**, p. 279-284; Tbilisi, publishing house
of the Tbilisi State University (in Russian).
Jointly with M.R.Levitin
and V.B.Lidskii.

31. *Forced vibrations of a shell filled with a viscous
compressible fluid*, Uspekhi Mat. Nauk **43**, no. 4, p. 164 (in
Russian).
Jointly with M.R.Levitin and V.B.Lidskii.

32. *Forced vibrations of a thin elastic shell filled with a viscous
compressible fluid*, Soviet Physics Doklady **34**, no. 3, p. 215-217.
Jointly with M.R.Levitin and V.B.Lidskii.

33. *Branching Hamiltonian billiards*, Soviet Mathematics Doklady
**38**, no. 1, p. 64-68. Jointly with Yu.G.Safarov.

34. *High-frequency radiation of a thin elastic shell*, Mechanics of
Solids **24**, no. 5, p. 163-174. Jointly with A.L.Gol'denveizer and
E.V.Nolde.

35. *Vibrations of a shell containing fluid*, International
Conference on Engineering Aero-Hydroelasticity (Prague, 1989), vol. **
2**, p. 185-190. Jointly with A.Gol'denveizer, J.Kaplunov and V.Lidskii.

36. *Equations of magnetoelasticity of thin shells. Statement of the
problem and error estimates*, preprint no. 400 of the Institute for
Problems in Mechanics of the USSR Academy of Sciences, 44 p. (in
Russian). Jointly with A.L.Gol'denveizer, J.D.Kaplunov,
M.R.Levitin,
D.G.Markushevich, E.V.Nolde and A.L.Radovinskii.

37. *Equations of magnetoelasticity of superconducting shells*,
Transactions of the 4
Symposium on Theoretical Problems of Magnetoelasticity (Yerevan, 1989),
p. 49-52; Yerevan, publishing house of the Yerevan State University (in
Russian).

38. *Two-term asymptotics of the spectrum of natural frequencies of a thin
elastic shell*, Soviet Mathematics Doklady **41**, no. 1, p.
108-112.

39. *On the problems of magnetoelasticity of thin superconducting
shells*, Transactions of the 15 USSR Conference on the Theory of
Plates and Shells (Kazan, 1990), vol. **1**, p. 265-271; Kazan,
publishing house of the Kazan State University (in Russian). Jointly
with M.R.Levitin.

40. *The asymptotic distribution of eigenvalues of differential
operators*, Lectures at the 14 School on Operator Theory in
Functional Spaces (Novgorod, 1989), part **2**, 114 pages; Novgorod,
publishing house of the Novgorod Pedagogical Institute (in Russian).
Jointly with Yu.G.Safarov.

41. *Tambour fractal: exemple d'une formule asymptotique a deux
termes pour la ``fonction de comptage''*, Comptes Rendus Acad. Sc.
Paris, 1990, vol. **311**, p. 867-872. Jointly with
J.Fleckinger.

42. *Distribution of free vibration frequencies in two- and
three-dimensional elastic bodies*, in Mechanics of Deformable
Solids (edited by N.Kh.Arutiunian, I.F.Obraztzov and V.Z.Parton), p.
227-242; *Hemisphere Publishing Corporation*. Jointly with
A.L.Gol'denveizer.

43. *One can hear the dimension of a connected fractal in* , in
Petkov & Lazarov: Integral Equations and Inverse Problems, p. 270-273;
*Longman Academic, Scientific & Technical* (1991).

44. *A class of nonlinear variational problems appearing in the theory
of magnetoelasticity of thin superconducting shells*, Nonlinearity **
4**, p. 821-833. Jointly with
A.Laptev
and
M.R.Levitin.

45. *Forced vibrations of a shell immersed in a viscous
compressible fluid*, Functional Analysis and its
Applications **25**, p. 309-311.
Jointly with M.R.Levitin
and V.B.Lidskii.

46. *Remarks on vibration of thin elastic shells and their numerical
computation*, Comptes Rendus Acad. Sc.
Paris, 1992, vol. **314**, Ser. 2, p. 445-452. Jointly with
E.Sanchez-Palencia.

47. *The asymptotic distribution of eigenvalues of differential
operators*, translation into English of the revised version of reference
40, in ``Spectral Theory of Operators'' (ed. S.Gindikin), American
Mathematical Society Translations, ser. 2, vol. **150** (1992), p. 55-111.
Jointly with Yu.G.Safarov.

48. *The distribution of eigenvalues of partial differential
operators*, Équations aux Dérivées
Partielles, Séminaire 1991-1992, Exposé noXVII 17 Mars 1992,
École Polytechnique, p. XVII-1 - XVII-17.

49. *Characteristic properties of distributions associated with the
wave group*, Journees Équations aux Dérivées
Partielles, Saint-Jean-De-Monts, 1992,
p. XV-1 - XV-14.

50. *On global representation of Lagrangian distributions and
solutions of hyperbolic equations*, preprint no. LiTH-MAT-R-92-25 of
Linköping University (Sweden), 1992; 54 pages. Jointly with
A.Laptev
and
Yu.Safarov.

51. *Global representation of Lagrangian distributions*, in ``Operator
Calculus and Spectral Theory'' (ed. M.Demuth, B.Gramsch and B.-W.Schulze),
series Operator Theory: Advances and Applications, vol. **57**,
Birkhäuser Verlag, 1992, p. 197-213. Jointly with
A.Laptev
and
Yu.Safarov.

52. *Vibration du Tambour Fractal*, Matapli (Bulletin SMAI --
Société de Mathématiques Appliquées et Industrielles), no. 32
Octobre 1992, p. 29-36. Jointly with
J.Fleckinger.

53. Book review (*Pseudodifferential operators on manifolds with
singularities* by B.-W.Schulze), Bulletin of
the London Mathematical Society, 1993, no. 113, vol. **25** part 2,
p. 203-204.

54. *An example of a two-term asymptotics for the ``counting
function'' of a fractal drum*,
Transactions of the American Mathematical Society, 1993, vol. **337**,
no. 1, p. 99-116. Jointly with
J.Fleckinger.

55. *Existence theorems for trapped modes*,
Journal of Fluid Mechanics, 1994, vol. **261**, p. 21-31. Jointly with
D.V.Evans
and
M.Levitin.

56. Mathematics, Soviet style. Book review (*Cubature formulas and
modern analysis: an introduction* by S.L.Sobolev), The Times Higher
Education Supplement, no. 1143, 30 September 1994, p. 25.

57. *On global representation of Lagrangian distributions and solutions
of hyperbolic equations*, Communications on Pure and Applied Mathematics,
1994, vol. **47**, no. 11, p. 1411-1456. Jointly with
A.Laptev
and
Yu.Safarov.

58. *Formula for the frequency counting function of a thin shell of
revolution for the case of a simple turning point*,
Functional Analysis and its Applications, 1994,
vol. **28**, no. 4, p. 282-284.
Jointly with A.G.Aslanyan and V.B.Lidskii.

59. *Construction of the wave group
for higher order elliptic boundary value
problems*, Équations aux Dérivées
Partielles, Séminaire 1994-1995, Exposé noİX 22 Novembre 1994,
École Polytechnique, p. IX-1 - IX-14.

60. Book review (*Degenerate Elliptic
Equations* by S.Levendorskii), Bulletin of
the London Mathematical Society, 1995, no. 125, vol. **27** part 2,
p. 198-199.

61. Book review (*Introduction to the general theory of singular
perturbations* by S.A.Lomov), Bulletin of
the London Mathematical Society, 1995, no. 125, vol. **27** part 2,
p. 201-202.

62. *Some examples of two-term spectral asymptotics for sets
with fractal boundary*,
series Operator Theory: Advances and Applications, vol. **78**
(ed. M.Demuth and B.-W.Schulze),
Birkhäuser Verlag, 1995, p. 227-233. Jointly with
M.Levitin.

63. *Vibrations of a shell submerged in fluid*,
in ``Spectral Analysis of Complex Structures'' (ed. E. Sanchez-Palencia),
Hermann, 1995, p. 159-171.

64. *Heat equation on the triadic von Koch snowflake: asymptotic and
numerical analysis*, Proceedings of the London
Mathematical Society, 1995, vol. **71**, p. 372-396.
Jointly with
J.Fleckinger
and
M.Levitin.

65. *The symbol of a Lagrangian distribution*,
Journees Équations aux Dérivées
Partielles, Saint-Jean-De-Monts, 1995,
p. V.1 - V.12.

66. *Heat content of the triadic von Koch snowflake*,
International Journal of Applied Science and Computations
1995, vol. **2**, , no. 2, p. 289-305.
Jointly with
J.Fleckinger
and
M.Levitin.

67. *Spectral asymptotics, renewal theorem, and the Berry conjecture
for a class of fractals*, Proceedings of the London
Mathematical Society, 1996, vol. **72**, p. 188-214.
Jointly with M.Levitin.

68. Book review (*Fourier Integral Operators* by J.J.Duistermaat,
V.W.Guillemin and L.Hörmander, and *Microlocal Analysis for
Differential Operators - An Introduction* by A.Grigis and J.Sjöstrand),
Bulletin of
the London Mathematical Society, 1996, no. 131, vol. **28** part 2,
p. 208-212.

69. *Vibrations of shells contacting fluid: asymptotic analysis*,
in ``Acoustic Interaction with Submerged Elastic Structures -- Part I''
(ed. A.Guran, J.Ripoche and F.Ziegler), World Scientific, 1996, p. 310-332.
Jointly with M.Levitin.

70. *On spectral pollution in the finite element approximation of thin
elastic ``membrane'' shells*, Numerische Mathematik, 1997,
vol. **75**, p. 473-500.
Jointly with J.Rappaz, J. Sanchez Hubert, and E. Sanchez Palencia.

71. *Edge resonance in an elastic semi-strip*,
Quarterly Journal of Mechanics and Applied Mathematics, 1998,
vol. **51** part 1, p. 1-13.
Jointly with I.Roitberg and T.Weidl.

72. Book review (*Elliptic boundary value problems
in domains with point singularities*
by V.A.Kozlov, V.G.Maz'ya and J.Rossmann),
Bulletin of
the London Mathematical Society, 1999, no. 150, vol. **31** part 3,
p. 370-371.

73. *The Dirac equation without spinors*, in ``Rostock
Conference on Functional Analysis, Partial Differential Equations
and Applications'' (ed. J.Rossmann, P.Takac and G.Wildenhain),
series Operator Theory: Advances and Applications, vol. **110**,
Birkhäuser Verlag, 1999, p. 133-152. Jointly with
D.M.Elton.
Available as preprint
math-ph/9808010.

74. *Victor Borisovich Lidskii (on his 75th
birthday)*, Russian Mathematical Surveys, 1999, vol. **54**,
no. 5, p. 1077-1085.
Jointly with M.S.Agranovich, V.I.Arnol'd, I.M.Gel'fand,
A.L.Gol'denveizer, A.G.Kostyuchenko, L.D.Kudryavtsev and M.I.Vishik.

75. *Trapped modes in a waveguide with a long obstacle*,
Journal of Fluid Mechanics, 2000, vol. **403**, p. 251-261.
Jointly with N.S.A.Khallaf and
L.Parnovski.

76. *Edge resonance in an elastic semi-infinite cylinder*,
Applicable Analysis, 2000, vol. **74**, no. 3-4, p. 479-495.
Jointly with A.Holst.

77. *Complex resonances in acoustic waveguides*,
Quarterly Journal of Mechanics and Applied Mathematics,
2000, vol. **53** part 3, p. 429-447.
Jointly with A.Aslanyan
and
L.Parnovski.

78. Book review (*Spectral theory and geometry*,
ed. E.B.Davies and Yu.Safarov),
Bulletin of the London Mathematical Society, 2000, vol. **32** issue 6,
p. 751-752.

79. *A metric-affine field model for the neutrino*,
in
``Noncommutative structures in mathematics and physics''
(ed. S.Duplij and J.Wess),
NATO Science Series II: Mathematics, Physics and Chemistry, vol. **22**,
Kluwer Academic Publishers, 2001, p. 427-439.

80. *Torsion waves in metric-affine field theory*,
Classical and Quantum Gravity,
2001, vol. **18**, p. 2317-2329.
Jointly with
A.D.King.
Available as preprint
gr-qc/0012046.

81. *Pseudoinstantons in metric-affine field theory*,
General Relativity and Gravitation,
2002, vol. **34**, p. 1239-1265.
Available as preprint
gr-qc/0108028.

82. *Pseudoinstantons in metric-affine field theory*,
in
``Quark confinement and the hadron spectrum V''
(ed. N.Brambilla and G.M.Prosperi),
World Scientific, 2003, p. 273-275.

83.
*The pseudoinstanton - a Lorentzian analogue of the
instanton*,
Proceedings of Institute of Mathematics of NAS of Ukraine,
2004, vol. **50** part 2, p. 981-985.

84.
*Quadratic non-Riemannian gravity*,
Journal of Nonlinear Mathematical Physics,
2004, vol. **11** Supplement, p. 204-216.

85.
*Quadratic metric-affine gravity*,
Annalen der Physik,
2005, vol. **14**, no. 4, p. 231-252.
The paper is a heavily revised version of preprint
gr-qc/0304028.

86.
*PP-waves with torsion and metric-affine gravity*,
Classical and Quantum Gravity,
2005, vol. **22**, p. 3961-3975.
Jointly with V.Pasic.
Available as preprint
gr-qc/0505157.

87.
*Teleparallel model for the neutrino*,
Physical Review D, 2007, vol. **75**, article number 025006 (6 pages).
The paper is a heavily revised version of preprint
gr-qc/0604011.

88.
*A teleparallel representation of the Weyl Lagrangian*,
International Journal of Geometric Methods in Modern Physics,
2007, vol. **4**, no. 2, p. 325-332.

89.
*A teleparallel representation of the Weyl Lagrangian*,
in
``Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity''
(in 3 volumes, editors H.Kleinert and R.T.Jantzen, series editor R.Ruffini),
World Scientific, 2008, part B, p. 1245-1247.
Available as preprint
gr-qc/0702020.

90.
*Dirac equation as a special case of Cosserat elasticity*,
in ``Analysis, Partial Differential Equations
and Applications - The Vladimir Maz'ya Anniversary Volume''
(ed. A.Cialdea, F.Lanzara and P.E.Ricci),
series Operator Theory: Advances and Applications, vol. **193**,
Birkhäuser Verlag, 2009, p. 15-29.
Jointly with J.Burnett and O.Chervova.
Available as preprint
arXiv:0812.3948.

91.
*Weyl's Lagrangian in teleparallel form*,
Journal of Mathematical Physics, 2009, vol. **50**, article number 102501 (17 pages).
Jointly with J.Burnett.
Available as preprint
arXiv:0901.1070.

92.
*Massless Dirac equation as a special case of Cosserat elasticity*,
Journal of the Association of Arab Universities
for Basic and Applied Sciences, 2009, vol. **7**, p. 25-42.
(Proceedings of the International Conference
on Recent Trends in Mathematical Sciences, Bahrain, 10-12 November 2008.)
Jointly with O.Chervova.
Available as preprint
arXiv:0902.1268.

93.
*The stationary Weyl equation and Cosserat elasticity*,
Journal of Physics A: Mathematical and Theoretical,
2010, vol. **43**, article number 335203 (14 pages).
Jointly with O.Chervova.
The paper is a heavily revised version of preprint
arXiv:1001.4726.

94. *Victor Borisovich Lidskii (1924-2008)*,
in ``Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)''
(ed. M.Levitin and D.Vassiliev),
series American Mathematical Society Translations - Series 2, vol. **231**,
American Mathematical Society,
2010, p. 1-5.
Jointly with M.Levitin.
Available as preprint
arXiv:1008.2669.

95. *Rotational elasticity*,
Quarterly Journal of Mechanics and Applied Mathematics,
2011, vol. **64**, p. 415-439.
Jointly with
C.G.Boehmer
and R.J.Downes.
Click
here for free online access.
The paper is a heavily revised version of preprint
arXiv:1008.3833.

96.
*Modelling the neutrino in terms of Cosserat elasticity*,
in
``Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity''
(in 3 volumes, editors Thibault Damour and Robert Jantzen, series editor Remo Ruffini),
World Scientific, 2012, part C, p. 2398-2400.
Jointly with O.Chervova.
Available as preprint
arXiv:1003.0574.

97. *Modelling the electron with Cosserat elasticity*,
Mathematika,
2012, vol. **58**, p. 349-370.
Jointly with J.Burnett.
The paper is a heavily revised version of preprint
arXiv:1007.3481.

98. *The spectral function of a first order elliptic system*,
Journal of Spectral Theory,
2013, vol. **3**, p. 317-360.
Jointly with O.Chervova and R.J.Downes.
Available as preprint
arXiv:1208.6015.

99. *Spectral asymmetry of the massless Dirac operator on a 3-torus*,
Journal of Mathematical Physics, 2013, vol. **54**, article number 111503 (18 pages).
Jointly with R.J.Downes and
M.Levitin.
Available as preprint
arXiv:1306.5689.

100. *Spectral theoretic characterization of the massless Dirac operator*,
Journal of the London Mathematical Society,
2014, vol. **89**, p. 301-320.
Jointly with O.Chervova and R.J.Downes.
Available as preprint
arXiv:1209.3510.

101. *Analysis as a source of geometry: a non-geometric representation of the Dirac equation*,
Journal of Physics A: Mathematical and Theoretical,
2015, vol. **48**, article number 165203 (19 pages).
Jointly with Yan-Long Fang.
This is an Open Access paper and it can downloaded
here.

102. *Analysis of first order systems of partial differential equations*,
to appear in Complex Analysis and Dynamical Systems VI, AMS Contemporary Mathematics Series.
Jointly with Yan-Long Fang.
Available as preprint
arXiv:1403.2663.

103. *Spectral theoretic characterization of the massless Dirac action*.
Jointly with R.J.Downes.
Preprint
arXiv:1401.1951.

The background on this page uses an illustration from [64].

**Updated 17 April 2015**