Metadata
Abstract
We study the essential self-adjointness for real principal type differential operators. Unlike the elliptic case, we need geometric conditions even for operators on the Euclidean space with asymptotically constant coefficients, and we prove the essential self-adjointness under the null non-trapping condition.
References
[BVW15] Asymptotics of radiation fields in asymptotically Minkowski space, Am. J. Math., Volume 137 (2015) no. 5, pp. 1293-1364 | DOI | MR | Zbl
[Chi02] Smoothing effects of dispersive pseudodifferential equations, Commun. Partial Differ. Equations, Volume 27 (2002) no. 9-10, pp. 1953-2005 | DOI | MR | Zbl
[DH72] Fourier integral operators. II, Acta Math., Volume 128 (1972) no. 3-4, pp. 183-269 | DOI | MR | Zbl
[GRHV16] The Feynman propagator on perturbations of Minkowski space, Commun. Math. Phys., Volume 342 (2016) no. 1, pp. 333-384 | DOI | MR | Zbl
[GS93] Nonelliptic Schrödinger equations, J. Nonlinear Sci., Volume 3 (1993) no. 2, pp. 169-195 | DOI | Zbl
[GT12] Strichartz estimates for the periodic non-elliptic Schrödinger equation, C. R. Math. Acad. Sci. Paris, Volume 350 (2012) no. 21-22, pp. 955-958 | DOI | Zbl
[GW19] The massive Feynman propagator on asymptotically Minkowski spacetimes, Amer. J. Math., Volume 19 (2019) no. 6, pp. 1501-1546 | DOI | MR | Zbl
[Hör85] Analysis of Linear Partial Differential Operators, Grundlehren der Mathematischen Wissenschaften, I-IV, Springer, 1983-1985 | Zbl
[IN09] Singularities of solutions to Schrödinger equation on scattering manifold, Am. J. Math., Volume 131 (2009) no. 6, pp. 1835-1865 | DOI | Zbl
[KPRV05] Variable coefficient Schrödinger flows for ultrahyperbolic operators, Adv. Math., Volume 196 (2005) no. 2, pp. 373-486 | DOI | Zbl
[Mel94] Spectral and scattering theory for the Laplacian on asymptotically Euclidian spaces, Spectral and scattering theory. Proceedings of the Taniguchi international workshop, held at Sanda, Hyogo, Japan (Lecture Notes in Pure and Applied Mathematics), Volume 161, Basel: Marcel Dekker, 1994, pp. 85-130 | MR | Zbl
[MT15] Strichartz estimates for non-elliptic Schrödinger equations on compact manifolds, Commun. Partial Differ. Equations, Volume 40 (2015) no. 6, pp. 1182-1195 | DOI | Zbl
[Nak05] Propagation of the homogeneous wave front set for Schrödinger equations, Duke Math. J., Volume 126 (2005) no. 2, pp. 349-367 | Zbl
[RS80] The Methods of Modern Mathematical Physics, I-IV, Academic Press Inc., 1972-1980 | Zbl
[Sal07] The Schrödinger equation type with a nonelliptic operator, Commun. Partial Differ. Equations, Volume 32 (2007) no. 1-3, pp. 209-228 | DOI | MR | Zbl
[Tai20] Strichartz estimates for non-degenerate Schrödinger equations, Math. Nachr., Volume 293 (2020) no. 4, pp. 774-793 | DOI | MR | Zbl
[Vas20] Essential self-adjointness of the wave operator and the limiting absorption principle on Lorentzian scattering spaces, J. Spectr. Theory, Volume 10 (2020) no. 2, pp. 439-461 | DOI | MR | Zbl
[VW18] Quantum fields from global propagators on asymptotically Minkowski and extended de Sitter spacetimes, Ann. Henri Poincaré, Volume 19 (2018) no. 5, pp. 1529-1586 | DOI | MR | Zbl
[Wan13] Periodic cubic hyperbolic Schrödinger equation on , J. Funct. Anal., Volume 265 (2013) no. 3, pp. 424-434 | DOI | MR | Zbl
[Zwo12] Semiclassical Analysis, Graduate Studies in Mathematics, 138, American Mathematical Society, 2012 | MR | Zbl