Selected Publications
Please note this page only lists selected publications by group members. Other publications can be found on group members' personal webpages.
Books
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A. Constantin, Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis, CBMS-NSF Regional Conference Series in Applied Mathematics, 81, SIAM, Philadelphia, 2011.
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S.G. Scott. Traces and Determinants of Pseudodifferential Operators, Oxford University Press, 2010.
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E.Shargorodsky, J.F.Toland, Bernoulli free-boundary problems. Mem. Amer. Math. Soc. 196 (2008), no. 914
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E.B.Davies, Linear operators and their spectra. Cambridge Studies in Advanced Mathematics, 106. Cambridge University Press, 2007
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E.B.Davies, Science in the looking glass. What do scientists really know? Oxford University Press, 2003.
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Yu.Safarov, D.Vassiliev, The asymptotic distribution of eigenvalues of partial differential operators, Translations of Mathematical Monographs, 155. American Mathematical Society, 1997.
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E.B.Davies, Spectral theory and differential operators. Cambridge Studies in Advanced Mathematics, 42. Cambridge University Press, 1995.
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E.B.Davies, Heat kernels and spectral theory. Cambridge Tracts in Mathematics, 92. Cambridge University Press, 1989.
Selected publications
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A. Constantin and J. Escher, Analyticity of periodic traveling free surface water waves with vorticity, Ann. of Math. (2) 173 (2011), no. 1, 559--568.
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A. Pushnitski: The Birman-Schwinger principle on the essential spectrum, J. Functional Analysis, vol. 261, 2053-2081 (2011).
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P. McKeag, Y. Safarov: Pseudodifferential operators on manifolds: an invariant approach. In Partial Differential Equations and Spectral Theory, 321-341, Oper. Theory Adv. Appl., 211 (2011).
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N. Filonov, Y. Safarov: On the relation between an operator and its self-commutator, J. Funct. Anal. 260, no. 10, 2902-2932 (2011).
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A. Constantin and W. Strauss, Pressure beneath a Stokes wave, Comm. Pure Appl. Math. 63 (2010), no. 4, 533--557.
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E.B. Davies, P.A. Incani: Spectral Properties of Matrices Associated with Some Directed Graphs, Proc. London Math. Soc. (3) 100 (2010) 55-90.
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A. Pushnitski, D. Yafaev: Spectral theory of discontinuous functions of self-adjoint operators and scattering theory, J. Functional Analysis, vol. 259, no. 8, 1950-1973 (2010).
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V. Buslaev, A. Pushnitski: The scattering matrix and associated formulas in Hamiltonian mechanics, Communications in Mathematical Physics, vol. 293, no.2, 563-588 (2010).
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N. Filonov, Y. Safarov: Asymptotic estimates for the difference between Dirichlet and Neumann counting functions, Funct. Anal. Appl. 44 , no. 4, 286–294 (2010).
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S. Scott: Eta Forms and determinant lines, Advances in Mathematics, Volume 225, 2517-2545 (2010) E. Shargorodsky: Toeplitz matrices with variable coefficients, pseudodifferential operators, and Strichartz's method, Math. Nachr. 283, 1, 126-138 (2010).
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E. Shargorodsky: Pseudospectra of semigroup generators, Bulletin LMS, 42, 6, 1031-1034 (2010).
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A. Constantin and D. Lannes, The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations, Arch. Ration. Mech. Anal. 192 (2009), no. 1, 165--186.
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E.B. Davies: Decomposing the Essential Spectrum, J. Functional Analysis, 257 (2009) 506–536.
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L. Hugues, I. Polterovich, Y. Safarov: Average growth of the spectral function on a Riemannian manifold, Comm. Partial Differential Equations 34, no. 4-6, 581-615 (2009).
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E. Shargorodsky: On the definition of pseudospectra, Bulletin LMS, 41, 3, 524-534 (2009).
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D. Damanik, A. Pushnitski, B. Simon: The analytic theory of matrix orthogonal polynomials, Surveys in Approximation Theory vol. 4, 1-85 (2008).
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E. Shargorodsky: On the level sets of the resolvent norm of a linear operator, Bulletin LMS, 40, 3, 493-504 (2008).
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S.Paycha, S.Scott: A Laurent expansion for regularized integrals of holomorphic symbols, Geom. and Funct. Anal. 17, 491 - 536 (2007) E.B. Davies, B. Simon: Eigenvalue Estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle, J. Approx. Theory 141 (2006) 189-213.