Translation-invariant estimates for operators with simple characteristics

Journal of Differential Equations - Tập 263 - Trang 5656-5695 - 2017
Eemeli Blåsten1, John Sylvester2
1HKUST Jockey Club Institute for Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
2Department of Mathematics, University of Washington, Seattle, WA 98195, USA

Tài liệu tham khảo

Agmon, 1975, Spectral properties of Schrödinger operators and scattering theory, Ann. Sc. Norm. Super. Pisa Cl. Sci., 2, 151 Agmon, 1976, Asymptotic properties of solutions of differential equations with simple characteristics, J. Anal. Math., 30, 1, 10.1007/BF02786703 Blåsten, 2014, Corners always scatter, Comm. Math. Phys., 331, 725, 10.1007/s00220-014-2030-0 Calderón, 1980, On an inverse boundary value problem, 65 Devaney, 2005, Time reversal imaging of obscured targets from multistatic data, IEEE Trans. Antennas and Propagation, 53, 1600, 10.1109/TAP.2005.846723 Faddeev, 1965, Growing solutions of the Schrödinger equation, Dokl. Akad. Nauk SSSR, 165, 514 Gel'fand, 1994, Discriminants, Resultants, and Multidimensional Determinants, 10.1007/978-0-8176-4771-1 Hörmander, 2005, The Analysis of Linear Partial Differential Operators. II. Differential Operators with Constant Coefficients Kenig, 1993, Small solutions to nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 10, 255, 10.1016/s0294-1449(16)30213-x Kenig, 1987, Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Math. J., 55, 329, 10.1215/S0012-7094-87-05518-9 Nachman, 1988, Reconstructions from boundary measurements, Ann. of Math., 128, 531, 10.2307/1971435 Alberto Ruiz, Harmonic analysis and inverse problems, June 2002, Lecture notes of the Summer School at Oulu, Finland. Serov, 2007, Fourier Transforms and Distributions, with Applications to Schrödinger Operators Sylvester, 2009, An estimate for the free Helmholtz equation that scales, Inverse Probl. Imaging, 3, 333, 10.3934/ipi.2009.3.333 Sylvester, 1987, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math., 125, 153, 10.2307/1971291 Tomas, 1975, A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc., 81, 477, 10.1090/S0002-9904-1975-13790-6 Uhlmann, 2009, Electrical impedance tomography and Calderón's problem, Inverse Probl., 25, 10.1088/0266-5611/25/12/123011