Annales Academię Scientiarum Fennicę
Mathematica
Volumen 35, 2010, 581-593

FREDHOLM EIGENVALUE FOR A QUASI-CIRCLE AND GRUNSKY FUNCTIONALS

Yuliang Shen

Soochow University, Department of Mathematics
Suzhou 215006, P.R. China; ylshen 'at' suda.edu.cn

Abstract. We give several new formulas of the least positive Fredholm eigenvalue for a quasi-circle, answering a problem posed recently by Kühnau. During the proof, we show that the Grunsky functionals corresponding to the two complementary domains of the quasi-circle are the same and equal to the reciprocal of the Fredholm eigenvalue.

2000 Mathematics Subject Classification: Primary 30C62; Secondary 30C55, 47B37.

Key words: Fredholm eigenvalue, quasi-circle, Grunsky functional.

Reference to this article: Y. Shen: Fredholm eigenvalue for a quasi-circle and Grunsky functionals. Ann. Acad. Sci. Fenn. Math. 35 (2010), 581-593.

Full document as PDF file

doi:10.5186/aasfm.2010.3536

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