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Upper and lower bounds for the Hilbert–Schmidt norm of a potential operator

  • Seyed ZoalroshdEmail author
Article
  • 6 Downloads

Abstract

We give upper and lower bounds for the Hilbert–Schmidt norm of logarithmic potential on a planar domain in terms of its area and inradius.

Keywords

Hilbert–Schmidt norm Logarithmic potential Polygon 

Mathematics Subject Classification

Primary 35S15 Secondary 35P99 

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Notes

Acknowledgements

I am very grateful to the referee for his/her various useful suggestions specially for introducing to the works of Exner, Harrell, Krejčiřík, Loss and Lotoreichik related to the topic of this note.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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