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133 Hamiltonian spectral flows, the Maslov index, and the stability of standing waves in the nonlinear Schroedinger equations, (with G. Cox, M. Curran, and R. Marangel).
132 Fredholm determinants, Evans functions and Maslov indices for partial differential equations, arXiv: 2206.07677 (with G. Cox and A. Sukhtayev).
131 Resolvent expansions for self-adjoint operators via boundary triplets, Bulletin of London Math. Soc., to appear, arXiv:2110.07434 (with S. Sukhtaiev).
130 First-order asymptotic perturbation theory for extensions of symmetric operators, arXiv:2012.00247 (with S. Sukhtaiev).
129 The essential spectrum of periodically-stationary solutions of the complex Ginzburg- Landau equation, Journal of Evolution Equations DOI 10.1007/s00028-020-00640-8, arXiv:2005.09176 (with John Zweck, Jeremy Marzuola, Chris K. R. T. Jones).
128 A dynamical approach to semilinear elliptic equations, Annales de l’Institut Henri Poincare C, Analyse Non Lineaire, 38 (2021), no. 2, 421–450. arXiv: 1907.09986 (with Margaret Beck, Graham Cox, Chris Jones, Alim Sukhtayev).
127 Exponential dichotomies for elliptic PDE on radial domains, In: W. Do ̈rfler et al. (eds.), Mathematics of Wave Phenomena, Trends in Mathematics, Springer, https://doi.org/10.1007/978-3-030-47174 4, arXiv: 1907.10372 (with Margaret Beck, Graham Cox, Chris Jones, Alim Sukhtayev).
126 Instability of unidirectional flows for the 2D α-Euler equations, Communications on Pure and Applied Analysis, 19 (2020) 2051–2079, doi:10.3934/cpaa.2020091, arXiv:1901.01367 (with Holger Dullin, Robert Marangell, Shibi Vasudevan, Joachim Worthington).
125 An index theorem for Schrodinger operators on metric graphs, In: Proceedings of the 2018 Arizona School of Analysis and Mathematical Physics, Contemporary Mathe- matics 741 (2020) 105 – 119 (with Selim Sukhtaiev).
124 Limits of quantum graph operators with shrinking edges, Advances in Mathematics 352 (2019) 632–669 (with Gregory Berkolaiko and Selim Sukhtaiev).
123 Eigenvalues of the linearized 2D Euler equations via Birman-Schwinger and Lin’s operators, J. Math. Fluid Mechanics 20 (2018) 1667–1680 (with Shibi Vasudevan).
122 Stability criteria for the 2D α-Euler equations, J. Math. Anal. Appl. 472 (2019) 1631 – 1659 (with Shibi Vasudevan).
121 Spectrum of non-planar traveling waves, Integral Eqns. Oper. Theory, (2018) 90: 30, https://doi.org/10.1007/s00020-018-2447-5 (with Anna Ghazaryan and Alin Pogan).
120. Stability of a planar front in a multidimensional reaction-diffusion system, SIAM Journal on Mathematical Analysis 50 (2018), 5569–5615 (with Anna Ghazaryan and Xinyao Yang).
119. Instability of pulses in gradient reaction–diffusion systems: a symplectic approach, Philosophical Transactions A, 376: 20170187; http://dx.doi.org/10.1098/rsta.2017.0187 (with Margaret Beck, Graham Cox, Chris Jones, Kelly McQuighan and Alim Sukhtayev)
118. The Selgrade decomposition for linear semiflows on Banach spaces, J. Dynamics Diff. Eqns. 31 (2019), no. 3, 1427–1456, arXiv:1701.05295 (with Alex Blumenthal).
117. The Maslov Index and the spectra of second order elliptic operators, Advances in Mathematics 329 (2018), 422–486 (with Selim Sukhtaiev).
116. Stable foliations near a traveling front for reaction diffusion systems, Discr. Cont. Dynam. Syst. B, 22 (2017), 3145–3165 (with R. Schnaubelt and Xinyao Yang).
115. The Maslov index for Lagrangian pairs on R2n, J. Math. Anal. Appl. 451 (2017), 794–821 (with P. Howard and A. Sukhtayev).
114. The Maslov and Morse indices for systmes of Schrodinger operators on R, Indiana University Math. J., 67 No. 5 (2018) (with P. Howard and A. Sukhtayev).
113. Hadamard-type formulas via the Maslov form, J. Evolution Eqns., 17 (1) (2016), 443–472. (with A. Sukhtayev).
112. Counting spectrum via the Maslov index for one dimensional θ-periodic Schrodinger operators, Proc. AMS, 145 (2017) 363 – 377 (with C. K. R. T. Jones and S. Sukhtaiev).
111. Some results on the entropy of nonautonomous dynamical systems, Dynamical Systems: An International Journal 31 (2016), no. 3, 251–279 (with C. Kawan).
110. The Morse and Maslov indices for Schrodinger operators, J. d’Analyse Mathem. 135 (2018), 345–387 (with A. Sukhtayev and S. Sukhtaiev).
109. The Morse and Maslov indices for multidimensional Schrodinger operators with matrix-valued potentials, Trans. Amer. Math. Soc., 368 (2016) 8145–8207 (with G. Cox, C. Jones and A. Sukhtayev).
108. Operator bounds employing complex interpolation revisited, Operator Theory: Advances and Applications, Collection of papers on the occasion of C. Batty 60-th birthday, W. Arendt R. Chill and Y. Tomilov (editors), Birkhauser, Operator Theory: Advances and Applications, Vol. 250, 213–239, 2015 (with F. Gesztesy, F. Sukochev and Y. Tomilov).
107. Stability of traveling waves in partly hyperbolic systems, Math. Model. Nat. Phenom. 8 (2013) 32 – 48 (with A. Ghazaryan and S. Schecter).
106. Finding eigenvalues of holomorphic Fredholm operator pencils using boundary value problems and contour integrals, Integral Eqns. Oper. Theory 78 (2014), 155 – 211 (with W.-J. Beyn and J. Rottmann-Matthes).
105. The Morse and Maslov indices for matrix Hill’s equations, Proc. Symp. Pure Math., 87 (2013) 205 – 233 (with C. Jones and R. Marangell).
104. Stability estimates for semigroups on Banach spaces, Discr. Cont. Dynam. Syst. Ser. A, (J. Goldstein’s 70-th anniversary issue), 33, No. 11-12, (2013), 5203 – 5216 (with V. A. Yurov).
103. The life and work of Nikolai Vasilevski. Recent trends in Toeplitz and pseudodifferential operators, pp. 1 – 14, In: Oper. Theory Adv. Appl., 210, Birkhauser Verlag, Basel, 2010 (with S. Grudsky and M. Shapiro).
102. The infinite dimensional Evans function, Journal of Functional Analysis 268 (2015) 1509–1586 (with A. Pogan).
101. The Evans function and the Weyl-Titchmarsh function, In: Special issue on stability of traveling waves, Discr. Cont. Dynam. Syst. Ser. S 5 (2012) 939 – 970 (with A. Sukhtayev).
100. Functional models of non-selfadjoint operators, strongly continuous semigroups, and matrix Muckenhoupt weights, Izvestiya Russian Acad. Sci.: Mathematics 75:2 (2011) 287 – 346 (with G. M. Gubreev).
99. Reduction principle and asymptotic phase for center manifolds of parabolic systems with nonlinear boundary conditions, J. Dynamics Diff. Eqns. 26 (2014), 243 – 266 (with R. Johnson and R. Schnaubelt).
98. Derivatives of the Evans function and (modified) Fredholm determinants for first order systems, Mathematische Nachrichten 284, No. 13, 1592 – 1638 (2011) (with M. Das).
97. The index formula and the spectral shift function for relatively trace class perturbations, Advances in Mathematics 227 (2011) 319 – 420 (with F. Gesztezy, K. A. Makarov, F. Sukochev and Y. Tomilov).
96. Stability of traveling waves for a class of reaction-diffusion systems that arise in chemical reaction models, SIAM J. Mathematical Analysis 42 (2010) 2434 – 2472 (with A. Ghazaryan and S. Schecter).
95. The algebraic multiplicity of eigenvalues and the Evans function revisited, In: M. Birman memorial volume, Mat. Model. Nat. Phenom., 5 (2010) 269 – 292 (with A. Sukhtayev).
94. Operator algebras and the Fredholm spectrum of advective equations of linear hydrodynamics, J. Functional Analysis 257 (2009) 3309 - 3328 (with R. Shvydkoy).
93. Stability of traveling waves for degenerate systems of reaction diffusion equations, Indiana University Math. J. 60 (2011), 443 – 472 (with A. Ghazaryan and S. Schecter).
92. Stability of gasless combustion fronts in one-dimensional solids, Archive Rational Mech. Anal. 198 (2010) 981 – 1030 (with A. Ghazaryan, S. Schecter, and A. de Souza).
91. Perturbations of strongly continuous operator semigroups, and matrix Muckenhoupt weights, Functional Analysis and Its Applications, 42 (2008) 234-238 (with G. Gubreev).
90. Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves, J. Math. Pures Appl., 90 (2008) 160-200 (with F. Gesztesy and K. Zumbrun).
89. The spectral mapping property of delay semigroups, Complex Anal. Oper. Theory, 2 (2008) 273-283 (with A. B ́atkai and T. Eisner).
88. The Dichotomy Theorem for evolution bi-families, J. Differential Equations, 245 (2008) 2267-2306. (with A. Pogan).
87. Center manifolds and dynamics near equilibria of quasilinear parabolic systems with fully nonlinear boundary conditions, Discr. Cont. Dynam. Syst. Ser. B, 9 (2008) 595-633 (with J. Pruss and R. Schnaubelt).
86. Scattering in a forked-shaped waveguide, Integral Eqns. Operator Theory, 61 (2008) 365-399 (with V. Pivovarchik).
85. Stable and unstable manifolds for quasilinear parabolic systems with fully nonlinear boundary conditions, J. Evolution Equations, 6 (2006) 535 – 576 (with J. Pruss and R. Schnaubelt).
84. Evans functions, Jost functions, and Fredholm determinants, Archive Rational Mech. Anal., 182 (2007) 361-421 (with F. Gesztesy and K. A. Makarov).
83. Non-self-adjoint operators, infinite determinants, and some applications, Russian J. Math. Phys. 12, No 4 (2005) 443-471 (with F. Gesztesy, M. Mitrea, and M. Zinchenko). Erratum in Russian J. Math. Phys. 12, 443–471 (2005).
82. Dichotomy and Fredholm properties of evolution equations, Journal Operator Theory, 58 (2007) 387-414 (with A. Pogan and R. Schnaubelt).
81. Fredholm determinants and the Evans function for difference equations, Banach Center Publications, 75 (2007) 111-135 (with D. Cramer).
80. Fredholm properties of evolution semigroups, Illinois J. Math., 48 (2004) 999-1020 (with Y. Tomilov).
79. Regularization and frequency domain stability of well posed systems, Mathematics of Control, Signals, and Systems, 17 (2005) 128-151 (with R. Schnaubelt and T. Randolph).
78. Fredholm differential operators with unbounded coefficients, J. Diff. Eqns., 208 (2005) 388-429 (with Y. Tomilov).
77. Spectral analysis of Darboux transformations for the focusing NLS hierarchy, J. d’Anal. Math., 93 (2004) 139-197 (with F. Gesztesy, R. Cascaval, and H. Holden).
76. Essential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents. J. Math. Fluid Mech., 7 (2005) 164–178 (with R. Shvidkoy).
75. Operator valued Fourier multipliers and stability of strongly continuous semigroups. Integral Eqns. Oper. Theory 51 (2005) 375-394 (with F. Rabiger).
74. The essential spectrum of the linearized 2D Euler operator is a vertical band. Contemp. Math. 327 (2003) 299–304. (with R. Shvidkoy).
73. Gearhart-Pruss Theorem in stability for wave equations: a survey. Lect. Notes Pure Appl. Math., 234 (2003) 105–120 (with D. Cramer).
72. Linear stability in an ideal incompressible fluid. Comm. Math. Phys., 233 (2003), 439–461 (with M. Vishik).
71. A sharp formula for the essential spectral radius of the Ruelle transfer operator on smooth and Hoelder spaces. Ergodic Theory & Dynamical Systems, 23 (2003) 175–191 (with V. M. Gundlach).
70. Hyperbolicity of semigroups and Fourier multipliers, In: Systems, Approximation, Singular Integral Operators, and Related Topics, International Workhop on Operator Theory and Applications, IWOTA 2000, eds. Alexander A. Borichev and Nikolai K. Nikolski, Oper. Theory Adv. Appl. 129 (2001) 341–364 (with R. Shvydkoy).