Some publications  of Vesselin PETKOV

 

Lower bounds on the number of scattering poles for several strictly convex obstacles,  Asymptotic Analysis, 30 (2002), 81-91.
 
Meromorphic continuation of the spectral shift function, (with V. Bruneau),  Duke Math. J.  116 (2003), 389-430.

 Eigenvalues of the reference operator and semiclassical resonances,  (with V. Bruneau),  J. Funct. Anal.  202 (2003), 571-590.

 Sojourn times, singularities of the scattering kernel and inverse problems, (with L. Stoyanov),  Inside Out: Inverse Problems and Applications, Ed. by G. Uhlmann, MSRI Publications,  vol. 47 (2003), pp. 297-332, Cambridge University Press.

Spectral shift function and resonances for non semi-bounded and Stark hamiltonians,  (with M. Dimassi), J. Math. Pures Appl, vol. 82 (2003). 1303-1342.

Resonances and semiclassical trace formulae,  Talk in the Workshop  "Maslov indices and semiclassical quantization", Regensburg, March 2004.

Semiclassical resonances and trace formulae for non semi-bounded Hamiltonians, (with M. Dimassi), Exposé Séminaire EDP, Ecole Polytechnique, 2003-2004.

Resonances for non-trapping time-periodic perturbations, (with J. F. Bony), J. Phys. A: Math. Gen.   37 (2004), 9439-9449.
 
Resonances for magnetic Stark Hamiltonians in two dimensional case, (with M. Dimassi), IMRN, 77 (2004), 4147-4179.

Global Strichartz estimates for the wave equation with time-periodic potentials, J. Funct. Anal.,  235  (2006), 357-376.

Estimates for the cut-off resolvent of the Laplacian for trapping obstacles, (with J. F. Bony), Exposé au Séminaire EDP, 2005-2006, Centre de Mathématiques, Ecole Polytechnique.

Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbaitons, Conference Phase Space Analysis of PDE, Pienza, 2005, Progress in Nonlinear Diff. Equations and their Applications, vol. 69 (2006), p. 267-285, Birhäuser, Boston.

Resolvent estimates and local energy decay for hyperbolic equations, (with J. F. Bony), Annali dell´Università di Ferrara - Sec. VII - Sci. Math. vol. 52, no.2 (2006), 233- 246.

Dynamical zeta function for several strictly convex obstacles, Canad. Math. Bulletin, vol. 51 (1), (2008), 100-113.

Exponential growth for the wave equation with compact time-periodic positive potential, (with F. Colombini and J. Rauch), Comm. Pure Appl. Math., vol. 62, (2009), 565-582.

Singularities of the scattering kernel related to trapping rays, (with L. Stoyanov),  Progress in Nonlineal Diff. Equations and their Applications, 78 (2009), Advances in Space Phase Analysis of  Partial Differential Equations, p. 235-251, Birkhauser, Boston.

Estimates of holomorphic functions in zero-free domians, (with A. Borichev), Archiv der Mathematik, 93 (2009), 47-58.

Correlations for pairs of periodic trajectories for open billiards, (with L. Stoyanov), Nonlinearity, 22 (2009), 2657-2679.

Spectral shift function for operators with crossed magnetic and electric fields, (with M. Dimassi), Rev. Math. Physics, 22 (2010), 355-380.

Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function, (with L. Stoyanov), Analysis & PDE, 3 (2010), 427-489.

Spectral problems for operators with crossed magnetic and electric fields, (with M. Dimassi), J. Phys. A: Math. Theor. 43 (2010), 474015.

Incoming and disappearing solutions for Maxwell's equations, (with F. Colombini and J. Rauch), Proc. AMS, 139 (2011), 2163-2173.

Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity, (with E. Bernardi and A. Bove), Journées EDP 2010, http://jedp.cedram.org/jedp-bin/browse?id=JEDP_2010___, Exp. No. 4, 13 p.

Distribution of periods of closed trajectories in exponentially shrinking intervals, (with L. Stoyanov), Commun. Math. Phys., 310 (2012), 675-704.

Semiclassical estimates of the cut-off resolvent for trapping perturbations, (with J. F. Bony), Journal of Spectral Theory, 3 (2013), 399-422.

Scattering problems for symmetric systems with dissipative boundary conditions, pp. 337-353 in Studies in Phase Space Analysis and Applications to PDEs, Progress in Nonlinear Differential Equations and their Applications, 84, Birkhauser, 2013.

Spectral problems for non elliptic symmetric systems with dissipative boundary conditions, (with F. Colombini and J. Rauch), Journal of Funct. Analysis, 267 (2014), 1637-1661.

Sharp large deviations for some hyperbolic systems (with L. Stoyanov), Ergodic Theory and Dynamical Systems, 35 (1) (2015), 249-273.

Cauchy problem for effectively hyperbolic operators with triple characteristics of variable multiplicity, (with E. Bernardi and A. Bove), JHDE, 12 (3), (2015), 535-579.

Location of eigenvalues for the wave equation with dissipative  boundary conditions, Inverse Problems and Imaging, 10 (4) (2016), 1111-1139.

Eigenvalues for Maxwell's equations with dissipative boundary conditions, (with F. Colombini and J. Rauch), Asymptotic Analysis, 99 (1-2) (2016), 105-124.

Ruelle transfer operators with two complex parameters and applications, (with L. Stoyanov), Discrete and Continuous Dynamical Systems-A, 36 (11) (2016), 6413-6451.

Localization of the interior transmission eigenvalues for a ball, (with G. Vodev), Inverse Problems and Imaging, 11 (2) (2017), 355-372.

Asymptotics of the number of interior transmission eigenvalues, (with G. Vodev), Journal of Spectral Theorry, vol. 7 (1) (2017), 1-31.


Location and Weyl formula for the eigenvalues of some non self-adjoint operators , pp. 181-203 in Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics, Springer INdAM Series 17 (2017).

Weyl formula for the negative dissipative eigenvalues of Maxwell's equations, (with F. Colombini), Archiv der Mathematik, 110 (2) (2018), 183-195.

Cauchy problem for effectively hyperbolic operators with triple characteristics, (with T. Nishitani), Journal de Math. Pures et Appl. vol. 123 (2019), 201-228.

Spectral estimates for Ruelle operators with two parameters and sharp large deviations, (with L. Stoyanov), Discrete and Continuous Dymanical Systems-A, 39 (11) (2019), 6391-6417.

Polynomial bounds on the Sobolev norms of the solutions of the nonlinear wave equation with time dependent potential, (with N. Tzvetkov), Archiv der Mathematik, 114 (1) (2020), 71-84.
 
Cauchy problem for hyperbolic operators with triple effective characteristics on the initial plane, (with T. Nishitani), Osaka Journal of Mathematics, 57 (3) (2020), 597-615.

Sharp large deviations for hyperbolic flows, (with L. Stoyanov), Annales Henri Poincaré, 21 (2020), 3791-3834.

On the nonlinear wave equation with time periodic potential, (with N. Tzvetkov), IMRN, 2021 (6) (2021), 4301-4323.

Absence of embedded eigenvalues for Hamiltonian with crossed magnetic and electric fields, (with M. Dimassi and M. Kawamoto), Rev. Math. Physics, 33 (6) (2021), 2150020.

Weyl formula for the eigenvalues of the dissipative acoustic operator,  Research in the Mathematical Sciences, 9 (1) (2022), Paper 5.

Asymptotic of the dissipative eigenvalues of Maxwell's equations, Asymptotic Analysis, 134 (3-4) (2023), 345-367.
 
On the number of poles of the dynamical zeta functions for billiard flow, Discrete and Continuous Dynamical Systems, 45 (9) (2025), 3174-3194.

Dirichlet dynamical zeta function for billiard flow, Archiv der Mathematik, 125 (2) (2025), 201-212.

Dynamical zeta functions for billiards, (with Y. Chaubet), Annales de l'Institut Fourier (Grenoble), Online first, 56 p.
 
Eigenvalues and resonances of dissipative acoustic operator for strictly convex obstacles, Preprint, 2023.

Corrigendum to "Spectral estimates for Ruelle operators with two parameters and sharp large deviations", (with L. Stoyanov),
Discrete and Continuous Dynamical Systems, 39 (11) (2019), 6391-6417.