Upper and lower bounds for the Hilbert–Schmidt norm of a potential operator
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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.
KeywordsHilbert–Schmidt norm Logarithmic potential Polygon
Mathematics Subject ClassificationPrimary 35S15 Secondary 35P99
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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.
- 6.Lotoreichik, V.: Spectral isoperimetric inequalities for singular interactions on open arcs. Applicable Analysis, 1–10 (2018)Google Scholar