Fundamental solutions for Schrödinger operators with general inverse square potentials

Abstract
In this paper, we clarify the fundamental solutions for Schrödinger operators given as (Formula presented.), where the potential V is a general inverse square potential in (Formula presented.) with (Formula presented.). In particular, letting (Formula presented.),(Formula presented.) where (Formula presented.), we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator (Formula presented.), which depend on the parameter t.

Citation
Chen H, Alhomedan S, Hajaiej H, Markowich P (2017) Fundamental solutions for Schrödinger operators with general inverse square potentials. Applicable Analysis: 1–24. Available: http://dx.doi.org/10.1080/00036811.2017.1286648.

Acknowledgements
H. Chen is supported by NNSF of China [grant number 11401270], [grant number 11661045]; the Jiangxi Provincial Natural Science Foundation [grant number 20161ACB20007]; SRF for ROCS, SEM from Ministry of Education in China.

Publisher
Informa UK Limited

Journal
Applicable Analysis

DOI
10.1080/00036811.2017.1286648

arXiv
1703.04053

Additional Links
http://www.tandfonline.com/doi/full/10.1080/00036811.2017.1286648http://arxiv.org/pdf/1703.04053

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