Finite propagation speed and kernel estimates for Schrödinger operators
HTML articles powered by AMS MathViewer
- by Christian Remling PDF
- Proc. Amer. Math. Soc. 135 (2007), 3329-3340 Request permission
Abstract:
We point out finite propagation speed phenomena for discrete and continuous Schrödinger operators and discuss various types of kernel estimates from this point of view.References
- Jean-Marc Bouclet, François Germinet, and Abel Klein, Sub-exponential decay of operator kernels for functions of generalized Schrödinger operators, Proc. Amer. Math. Soc. 132 (2004), no. 9, 2703–2712. MR 2054797, DOI 10.1090/S0002-9939-04-07431-3
- Jeff Cheeger, Mikhail Gromov, and Michael Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geometry 17 (1982), no. 1, 15–53. MR 658471
- E. W. Cheney, Introduction to approximation theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0222517
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
- Lawrence C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol. 19, American Mathematical Society, Providence, RI, 1998. MR 1625845
- François Germinet, Alexander Kiselev, and Serguei Tcheremchantsev, Transfer matrices and transport for Schrödinger operators, Ann. Inst. Fourier (Grenoble) 54 (2004), no. 3, 787–830 (English, with English and French summaries). MR 2097423
- François Germinet and Abel Klein, Operator kernel estimates for functions of generalized Schrödinger operators, Proc. Amer. Math. Soc. 131 (2003), no. 3, 911–920. MR 1937430, DOI 10.1090/S0002-9939-02-06578-4
- Alexander Kiselev, Imbedded singular continuous spectrum for Schrödinger operators, J. Amer. Math. Soc. 18 (2005), no. 3, 571–603. MR 2138138, DOI 10.1090/S0894-0347-05-00489-3
- Peter D. Lax and Ralph S. Phillips, Scattering theory, 2nd ed., Pure and Applied Mathematics, vol. 26, Academic Press, Inc., Boston, MA, 1989. With appendices by Cathleen S. Morawetz and Georg Schmidt. MR 1037774
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419
- Michael Reed and Barry Simon, Methods of modern mathematical physics. III, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. Scattering theory. MR 529429
- Christian Remling, Schrödinger operators and de Branges spaces, J. Funct. Anal. 196 (2002), no. 2, 323–394. MR 1943095, DOI 10.1016/S0022-1236(02)00007-1
- Christian Remling, Universal bounds on spectral measures of one-dimensional Schrödinger operators, J. Reine Angew. Math. 564 (2003), 105–117. MR 2021036, DOI 10.1515/crll.2003.086
- Theodore J. Rivlin, An introduction to the approximation of functions, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1969. MR 0249885
- Walter Rudin, Real and complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1987. MR 924157
- Adam Sikora, On-diagonal estimates on Schrödinger semigroup kernels and reduced heat kernels, Comm. Math. Phys. 188 (1997), no. 1, 233–249. MR 1471338, DOI 10.1007/s002200050163
- Barry Simon, Schrödinger operators in the twentieth century, J. Math. Phys. 41 (2000), no. 6, 3523–3555. MR 1768631, DOI 10.1063/1.533321
- A. F. Timan, Theory of approximation of functions of a real variable, A Pergamon Press Book, The Macmillan Company, New York, 1963. Translated from the Russian by J. Berry; English translation edited and editorial preface by J. Cossar. MR 0192238
Additional Information
- Christian Remling
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019-0315
- MR Author ID: 364973
- Email: cremling@math.ou.edu
- Received by editor(s): January 27, 2006
- Received by editor(s) in revised form: July 18, 2006
- Published electronically: June 20, 2007
- Communicated by: Joseph A. Ball
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3329-3340
- MSC (2000): Primary 81Q10, 35J10, 47B39, 47F05
- DOI: https://doi.org/10.1090/S0002-9939-07-08857-0
- MathSciNet review: 2322765