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Monatshefte für Mathematik

, Volume 168, Issue 2, pp 253–266 | Cite as

Global estimates of fundamental solutions for higher-order Schrödinger equations

  • JinMyong Kim
  • Anton Arnold
  • Xiaohua Yao
Article

Abstract

In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schrödinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish related L p L q estimates on the Schrödinger solution. These estimates extend known results from the literature and are sharp. This result was lately already generalized to a degenerate case (cf. [4]).

Keywords

Oscillatory integral Higher-order Schrödinger equation Fundamental solution estimate 

Mathematics Subject Classification (2000)

42B20 42B37 35Q41 35B65 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institut für Analysis und Scientific ComputingTechnische Universität WienWienAustria
  2. 2.Department of MathematicsKim Il Sung UniversityPyongyangDPR Korea
  3. 3.Institut für Analysis und Scientific ComputingTechnische Universität WienWienAustria
  4. 4.Department of MathematicsCentral China Normal UniversityWuhanPeople’s Republic of China

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