id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
8s45q813k6n	Steven Edward Broad	Index formulas for higher order Loewner vector fields	2010		.txt	text/plain	209	8	54	Structurally, our index formula provides a defect term for Loewner's conjecture containing geometric data extracted from Hessian-like objects associated with higher order derivatives of f. In particular, our index formula computes the Fredholm index of the Toeplitz operator on the unit circle whose symbol is the nth order Cauchy-Riemann derivative of f. Recent work of F. Xavier produced a formula for computing the index of such vector fields in the case n = 2 using data about the Hessian of f.	cache/8s45q813k6n.txt	txt/8s45q813k6n.txt