Books

Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008), edited by M Levitin and D Vassiliev, American Mathematical Society Translations - Series 2, Advances in the Mathematical Sciences, volume 231, 2010; 180 pp.
L Boulton and M Levitin, Trends and Tricks in Spectral Theory, Ediciones IVIC, Caracas, 2007; 99 pp. ISBN 978-980-261-086-0.

 

Papers and Preprints

Where available, links to the final published texts are provided; archived preprints (also linked) may differ from final versions. Hovering the mouse over the word "Abstract" should show the abstract of the paper on the right top (doesn't work in IE).

Y-L Fang, Michael Levitin, and D Vassiliev, Spectral analysis of the Dirac operator on a 3-sphere.
A R Gover, A Hassannezhad, D Jakobson, and M Levitin, Zero and negative eigenvalues of the conformal Laplacian, to appear in Journal of Spectral Theory.
M Levitin and M Seri, Accumulation of complex eigenvalues of an indefinite Sturm-Liouville operator with a shifted Coulomb potential, Operators and Matrices 10 (2014), 223–245.
E B Davies and M Levitin, Spectra of a class of non-self-adjoint matrices, Linear Algebra and its Applications 448 (2014), 55–84.
R J Downes, M Levitin and D Vassiliev, Spectral asymmetry of the massless Dirac operator on a 3-torus, J. of Mathematical Physics 54, Number 11, 111503 (2013).
D M Elton, M Levitin and I Polterovich, Eigenvalues of a one-dimensional Dirac operator pencil, Annales Henri Poincaré (2013).
M Levitin and D Vassiliev, Victor Borisovich Lidskii (1924-2008), in Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008), edited by M Levitin and D Vassiliev, American Mathematical Society Translations - Series 2, Advances in the Mathematical Sciences, volume 231, 2010, 1-6.
M Levitin, A Sobolev, and D Sobolev, On the near periodicity of eigenvalues of Toeplitz matrices, in Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008), edited by M Levitin and D Vassiliev, American Mathematical Society Translations - Series 2, Advances in the Mathematical Sciences, volume 231, 2010, 115-126.
L Boulton, M Levitin, and M Marletta, On a class of nonselfadjoint periodic boundary value problems with discrete real spectrum, in Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008), edited by M Levitin and D Vassiliev, American Mathematical Society Translations - Series 2, Advances in the Mathematical Sciences, volume 231, 2010, 59-66.
PdfPDF (arXiv:math)
L Boulton, M Levitin, and M Marletta, On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities, Journal of Differential Equations, 249 (2010), 3081-3098.
R Benguria, M Levitin, and L Parnovski, Fourier transform, null variety, and Laplacian's eigenvalues, Journal of Functional Analysis 257 (2009), 2088-2123.
M Levitin and M Marletta, A simple method of calculating eigenvalues and resonances in domains with infinite regular ends, Proc. Royal Soc. Edinburgh, 138A (2008), 1043-1065.
M Levitin and L Parnovski, On the principal eigenvalue of a Robin problem with a large parameter, Math. Nachrichten, 281 (2008), 272-281.
L Boulton and M Levitin, On approximation of the eigenvalues of perturbed periodic Schroedinger operators, J. Phys. A: Math. Gen., 40 (2007), 9319-9329.
M Levitin, L Parnovski, and I Polterovich, Isospectral domains with mixed boundary conditions, J. Phys. A: Math. Gen., 39 (2006), 2073-2082.
D Jakobson, M Levitin, N Nadirashvili, and I Polterovich, Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond, J. Comp. and Appl. Math. 194 (2006), 141-155.
D Jakobson, M Levitin, N Nadirashvili, N Nigam, and I Polterovich, How large can the first eigenvalue be on a surface of genus two?, Int. Math. Res. Notices 2005:63 (2005), 3967-3985.
E R Johnson, M Levitin, and L Parnovski, Existence of eigenvalues of a linear operator pencil in a curved waveguide --- localized shelf waves on a curved coast, SIAM J. Math. Anal. 37, issue 5 (2006),1465-1481.
M Levitin and E Shargorodsky, Spectral pollution and second order relative spectra for self-adjoint operators, IMA J. Numer. Analysis 24 (2004), 393-416.
M Levitin and R Yagudin, Range of the first three eigenvalues of the planar Dirichlet Laplacian, LMS J. Comput. Math. 6 (2003), 1-17.
M Levitin and L Parnovski, Trace identities and universal estimates for eigenvalues of linear pencils, in Elliptic and Parabolic Problems, Proceedings of the IV European Conference (Rolduc/Gaeta 2001), edited by J Bemelmans, etc, World Scientific (2002), 160-164.
M Levitin and L Parnovski, Commutators, spectral trace identities, and universal estimates for eigenvalues, J. Functional Analysis 192 (2002), 425-445.
M Levitin, Dirichlet Laplacian, in Encyclopaedia of Mathematics, Kluwer (2000).
PdfPDF (this site)
M S Agranovich, B A Amosov and M Levitin, Spectral problems for the Lamé system with spectral parameter in boundary bonditions on smooth or nonsmooth boundary, Russian Jour. Math. Physics 6 (1999), 247-281.
M Levitin, Dirichlet and Neumann heat invariants for Euclidean balls, Differential Geometry and Applicat. 8 (1998), 35-46.
M Levitin, Fourier Tauberian theorems, Appendix in the monograph by Yu Safarov and D Vassiliev, The asymptotic distribution of eigenvalues of partial differential operators , Series Translations of Mathematical Monographs, vol. 55, American Mathematical Society, Providence, R. I. (1997), 297-305.
M van den Berg and M Levitin, Functions of Weierstrass type and spectral asymptotics for iterated sets, Quarter. J. Math. Oxford (2) 47 (1996), 493-509.
M Levitin and D Vassiliev, Vibrations of shells contacting fluid: asymptotic analysis, Acoustic Interaction with Submerged Elastic Structures, eds. A Guran, J Ripoche and F Ziegler (Series on Stability, Vibration and Control of Systems, Series B: vol 5), World Scientific, Singapore, Part 1 (1996), 310-332.
M Levitin and D Vassiliev, Spectral asymptotics, renewal theorem, and the Berry conjecture for a class of fractals, Proc. London Math. Soc. (3) 72 (1996), 178-214.
M Levitin and D Vassiliev, Some examples of two-term spectral asymptotics for sets with fractal boundary, Operator Theory: Advances and Applications 78, Birkhäuser, Basel (1995), 227-233.
J Fleckinger, M Levitin and D Vassiliev, Heat equation on the triadic von Koch snowflake: asymptotic and numerical analysis, Proc. London Math. Soc. (3) 71 (1995), 372-396.
M Levitin, Exterior spectral problem for the Douglis-Nirenberg elliptic dissipative operator, Spectral Analysis of Complex Structures, ed. E Sanchez-Palencia, Hermann, Paris (1995), 59-69.
D V Evans, M Levitin and D Vassiliev , Existence theorems for trapped modes, J. Fluid Mech. 261 (1994), 21-31.
M Levitin, Vibrations of a viscous compressible fluid in bounded domains: spectral properties and asymptotics, Asymptotic Analysis 7 (1993), 15-35.
M Levitin, On a spectrum of a generalized Cosserat problem, C. R. Acad. Sci. Paris Série I 315 (1992), 925-930.
M Levitin, Vibrations of a viscous compressible fluid in bounded and unbounded domains, Mathematical Methods in Fluid Mechanics (Lisbon, 1991), Edited by J. F. Rodrigues and A. Sequeira. Pitman Research Notes in Mathematics Series 274, Longman Scientific & Technical, Harlow, 251-255.
D Vassiliev, M Levitin, and V Lidskii, Forced oscillations of a shell immersed in a viscous compressible fluid, Funktsional. Anal. i Prilozhen. 25 (1991), no. 4, 93-95 (Russian); translation in Funct. Anal. Appl. 25 (1991), no. 4, 309-311.
D Beilin, M Levitin, and V Polyakov, Interaction of a truncated spherical shell with an air stream parallel to the base , Building Mechanics and Analysis of Constructions 33, no. 1 (1991), 17-23 (in Russian).
A Laptev, M Levitin, and D Vassiliev , A class of nonlinear variational problems arising in the theory of magnetoelasticity of thin superconducting shells , Nonlinearity 4 (1991), 821-833.
D Vassiliev, M Levitin, and V Lidskii, Forced oscillations of a thin elastic shell that is filled with a viscous compressible fluid , Doklady AN SSSR 305, no. 2 (1989), 329-332 (in Russian); English translation in Soviet Physics Doklady 34, no. 3 (1989), 215-217.
M Levitin, On the spectrum of natural oscillations of a shell filled with a viscous compressible fluid, Doklady AN SSSR 295, no. 6 (1987), 1355-1358 (in Russian); English translation in Soviet Physics Doklady 32, no. 8 (1987), 638-639.
M Levitin, Free vibrations of a shell filled with a viscous fluid, Mathematical Methods of Control and Data-Processing, Moscow Institute of Physics and Technology Publishing House, Moscow (1986), 132-135 (in Russian).
M Levitin and A Sudakov, Eigenvalues of a problem on the semi-axis with constant coefficients , Mathematical Methods of Control and Data-Processing, Moscow Institute of Physics and Technology Publishing House, Moscow (1985), 48-53 (in Russian).