@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",

}