A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS
- 1 June 2001
- journal article
- Published by World Scientific Pub Co Pte Ltd in Reviews in Mathematical Physics
- Vol. 13 (6) , 717-754
- https://doi.org/10.1142/s0129055x01000843
Abstract
Results are obtained on resolvent expansions around zero energy for Schrödinger operators H=-Δ+V(x) on L2(Rm), where V(x) is a sufficiently rapidly decaying real potential. The emphasis is on a unified approach, valid in all dimensions, which does not require one to distinguish between ∫V(x)dx=0 and ∫V(x)dx≠0 in dimensions m=1,2. It is based on a factorization technique and repeated decomposition of the Lippmann–Schwinger operator. Complete results are given in dimensions m=1 and m=2.Keywords
This publication has 7 references indexed in Scilit:
- L p -Boundedness of Wave Operators for¶Two Dimensional Schrödinger OperatorsCommunications in Mathematical Physics, 1999
- Decay estimates for Schrödinger operatorsCommunications on Pure and Applied Mathematics, 1991
- Spectral properties of Schrödinger operators and time-decay of the wave functions. Results in L2(R4)Journal of Mathematical Analysis and Applications, 1984
- Asymptotic expansions in time for solutions of Schrödinger-type equationsJournal of Functional Analysis, 1982
- Spectral properties of Schrödinger operators and time-decay of the wave functions results in L2(Rm), m≥5Duke Mathematical Journal, 1980
- Spectral properties of Schrödinger operators and time-decay of the wave functionsDuke Mathematical Journal, 1979
- ON EXTERIOR ELLIPTIC PROBLEMS POLYNOMIALLY DEPENDING ON A SPECTRAL PARAMETER, AND THE ASYMPTOTIC BEHAVIOR FOR LARGE TIME OF SOLUTIONS OF NONSTATIONARY PROBLEMSMathematics of the USSR-Sbornik, 1973