Smoothing effects of Schrödinger evolution groups on Riemannian manifolds

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Smoothing effects of Schrödinger evolution groups on Riemannian manifolds

Shin-ichi Doi

Source: Duke Math. J. Volume 82, Number 3 (1996), 679-706.

First Page: Show

Primary Subjects: 58G99

Secondary Subjects: 58D25, 58F17

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077245257
Mathematical Reviews number (MathSciNet): MR1387689
Zentralblatt MATH identifier: 0870.58101
Digital Object Identifier: doi:10.1215/S0012-7094-96-08228-9

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References

[1] M. Ben-Artzi, Global estimates for the Schrödinger equation, J. Funct. Anal. 107 (1992), no. 2, 362–368.

Mathematical Reviews (MathSciNet): MR93e:35044

Zentralblatt MATH: 0774.35019

Digital Object Identifier: doi:10.1016/0022-1236(92)90113-W

[2] M. Ben-Artzi and A. Devinatz, Local smoothing and convergence properties of Schrödinger type equations, J. Funct. Anal. 101 (1991), no. 2, 231–254.

Mathematical Reviews (MathSciNet): MR92k:35064

Zentralblatt MATH: 0762.35022

Digital Object Identifier: doi:10.1016/0022-1236(91)90157-Z

[3] J. Bergh and J. Löfström, Interpolation Spaces. an Introduction, Grundlehren der Mathematischen Wissenschaften, vol. 223, Springer-Verlag, Berlin, 1976.

Mathematical Reviews (MathSciNet): MR58:2349

Zentralblatt MATH: 0344.46071

[4] P. Constantin and J. C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988), no. 2, 413–439.

Mathematical Reviews (MathSciNet): MR89d:35150

Zentralblatt MATH: 0667.35061

Digital Object Identifier: doi:10.2307/1990923

JSTOR: links.jstor.org

[5] P. Constantin and J. C. Saut, Local smoothing properties of Schrödinger equations, Indiana Univ. Math. J. 38 (1989), no. 3, 791–810.

Mathematical Reviews (MathSciNet): MR91e:35167

Zentralblatt MATH: 0712.35022

Digital Object Identifier: doi:10.1512/iumj.1989.38.38037

[6] S. Doi, On the Cauchy problem for Schrödinger type equations and the regularity of solutions, J. Math. Kyoto Univ. 34 (1994), no. 2, 319–328.

Mathematical Reviews (MathSciNet): MR95g:35190

Zentralblatt MATH: 0807.35026

Project Euclid: euclid.kjm/1250519013

[7] M. P. Gaffney, The harmonic operator for exterior differential forms, Proc. Nat. Acad. Sci. U. S. A. 37 (1951), 48–50.

Mathematical Reviews (MathSciNet): MR13,987b

Zentralblatt MATH: 0042.10205

Digital Object Identifier: doi:10.1073/pnas.37.1.48

JSTOR: links.jstor.org

[8] N. Hayashi, K. Nakamitsu, and M. Tsutsumi, On solutions of the initial value problem for the nonlinear Schrödinger equations in one space dimension, Math. Z. 192 (1986), no. 4, 637–650.

Mathematical Reviews (MathSciNet): MR88b:35175

Zentralblatt MATH: 0617.35025

Digital Object Identifier: doi:10.1007/BF01162710

[9] N. Hayashi, K. Nakamitsu, and M. Tsutsumi, On solutions of the initial value problem for the nonlinear Schrödinger equations, J. Funct. Anal. 71 (1987), no. 2, 218–245.

Mathematical Reviews (MathSciNet): MR88e:35162

Zentralblatt MATH: 0657.35033

Digital Object Identifier: doi:10.1016/0022-1236(87)90002-4

[10]¹ L. Hörmander, The analysis of linear partial differential operators. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983.

Mathematical Reviews (MathSciNet): MR85g:35002a

Zentralblatt MATH: 0521.35001

[10]² L. Hörmander, The analysis of linear partial differential operators. III, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985.

Mathematical Reviews (MathSciNet): MR87d:35002a

Zentralblatt MATH: 0601.35001

[11] W. Ichinose, On $L\sp 2$ well posedness of the Cauchy problem for Schrödinger type equations on the Riemannian manifold and the Maslov theory, Duke Math. J. 56 (1988), no. 3, 549–588.

Mathematical Reviews (MathSciNet): MR89g:58203

Zentralblatt MATH: 0713.58055

Digital Object Identifier: doi:10.1215/S0012-7094-88-05623-2

Project Euclid: euclid.dmj/1077306717

[12] K. Kajitani, The Cauchy problem for Schrödinger type equations with variable coefficients, preprint.

Mathematical Reviews (MathSciNet): MR1484618

Digital Object Identifier: doi:10.2969/jmsj/05010179

Project Euclid: euclid.jmsj/1225376794

[13] T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Studies in applied mathematics, Adv. Math. Suppl. Stud., vol. 8, Academic Press, New York, 1983, pp. 93–128.

Mathematical Reviews (MathSciNet): MR86f:35160

Zentralblatt MATH: 0549.34001

[14] T. Kato and K. Yajima, Some examples of smooth operators and the associated smoothing effect, Rev. Math. Phys. 1 (1989), no. 4, 481–496.

Mathematical Reviews (MathSciNet): MR91i:47013

Zentralblatt MATH: 0833.47005

Digital Object Identifier: doi:10.1142/S0129055X89000171

[15] H. Kumano-go, Pseudodifferential operators, MIT Press, Cambridge, Mass., 1981.

Mathematical Reviews (MathSciNet): MR84c:35113

Zentralblatt MATH: 0489.35003

[16] S. Mizohata, Some remarks on the Cauchy problem, J. Math. Kyoto Univ. 1 (1961/1962), 109–127.

Mathematical Reviews (MathSciNet): MR30:353

Zentralblatt MATH: 0104.31903

Project Euclid: euclid.kjm/1250525109

[17] M. Reed and B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1975.

Mathematical Reviews (MathSciNet): MR58:12429b

Zentralblatt MATH: 0308.47002

[18] P. Sjölin, Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), no. 3, 699–715.

Mathematical Reviews (MathSciNet): MR88j:35026

Zentralblatt MATH: 0631.42010

Digital Object Identifier: doi:10.1215/S0012-7094-87-05535-9

Project Euclid: euclid.dmj/1077306171

[19] W. Strauss, Smoothing of dispersive waves, Journées “Équations aux Dérivées Partielles” (Saint-Jean-de-Monts, 1993), École Polytech., Palaiseau, 1993, Exp. No. XIV, 5.

Mathematical Reviews (MathSciNet): MR94g:35061

Zentralblatt MATH: 0818.35098

[20] K. Yajima, On smoothing property of Schrödinger propagators, Functional-analytic methods for partial differential equations (Tokyo, 1989), Lecture Notes in Math., vol. 1450, Springer, Berlin, 1990, pp. 20–35.

Mathematical Reviews (MathSciNet): MR92e:35060

Zentralblatt MATH: 0725.35084

Digital Object Identifier: doi:10.1007/BFb0084896

[21] M. Yamazaki, On the microlocal smoothing effect of dispersive partial differential equations. I. Second-order linear equations, Algebraic analysis, Vol. II, Academic Press, Boston, MA, 1988, pp. 911–926.

Mathematical Reviews (MathSciNet): MR90i:35054

Zentralblatt MATH: 0683.35010

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