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]).
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Communicated by A. Jüngel.
This work was supported by the Postdoctoral Science Foundation of Huazhong University of Science and Technology in China and the Eurasia-Pacific Uninet scholarship for post-docs in Austria. The second author was supported by the FWF (project I 395-N16). The third author was supported by NSFC (No. 10801057), the Key Project of Chinese Ministry of Education (No. 109117), NCET-10-0431, and CCNU Project (No. CCNU09A02015).
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Kim, J., Arnold, A. & Yao, X. Global estimates of fundamental solutions for higher-order Schrödinger equations. Monatsh Math 168, 253–266 (2012). https://doi.org/10.1007/s00605-011-0350-0
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DOI: https://doi.org/10.1007/s00605-011-0350-0