Annales Academię Scientiarum Fennicę

Mathematica

Volumen 35, 2010, 291-307

# THE DERIVATIVE OF THE NEHARI FUNCTIONAL

## Eric Schippers

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.

Full document as PDF file

doi:10.5186/aasfm.2010.3518

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