@inproceedings{6059ef077f3947a3bb696987aa4641ea,
title = "Convexity of ranges and connectedness of level sets of quadratic forms",
abstract = "O. Toeplitz and F. Hausdorff proved that the range of any quadratic form on the unit sphere S of an inner product space X is convex and the level sets of any Hermitian form on S are connected. We consider the question: Which subsets of X, besides S, have these properties?",
keywords = "Connectedness, Convexity, Numerical range, Quadratic forms, Toeplitz-Hausdorff Theorem",
author = "I. Feldman and N. Krupnik and A. Markus",
note = "Publisher Copyright: {\textcopyright} 2009 Birkh{\"a}user Verlag Basel/Switzerland.; International Conference on Characteristic functions and transfer functions in operator theory and system theory, 2007 ; Conference date: 09-07-2007 Through 13-07-2007",
year = "2010",
month = jan,
day = "1",
doi = "10.1007/978-3-0346-0183-2_8",
language = "English",
isbn = "9783034601825",
series = "Operator Theory: Advances and Applications",
publisher = "Springer International Publishing",
pages = "149--179",
editor = "Daniel Alpay and Victor Vinnikov",
booktitle = "Characteristic Functions, Scattering Functions and Transfer Functions",
}