Annales Academię Scientiarum Fennicę
Mathematica
Volumen 35, 2010, 291-307
University of Manitoba, Department of Mathematics
Winnipeg, Manitoba, R3T 2N2 Canada; eric_schippers 'at' umanitoba.ca
Abstract. The Nehari functional assigns a number to subdomains of a fixed domain. For each choice of a certain singularity function, one obtains a different functional. In the case that the fixed outer domain is the unit disc, and the singularity is at the origin, we compute the derivative of Nehari's functional using a time-reversed Loewner equation and the power matrix. At an extremal, the derivative of Nehari's functional has a very simple form in terms of a quadratic differential associated with the singularity function.
2000 Mathematics Subject Classification: Primary 30C75, 30C55.
Key words: Dirichlet energy, Dirichlet space, bounded univalent functions, monotonicity, subordination, Loewner method, power matrix, extremal problems.
Reference to this article: E. Schippers: The derivative of the Nehari functional. Ann. Acad. Sci. Fenn. Math. 35 (2010), 291-307.
doi:10.5186/aasfm.2010.3518
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