Convexity of ranges and connectedness of level sets of quadratic forms

I. Feldman; N. Krupnik; A. Markus

doi:10.1007/978-3-0346-0183-2_8

Convexity of ranges and connectedness of level sets of quadratic forms

I. Feldman
, N. Krupnik
, A. Markus

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

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.

Original language	English
Title of host publication	Characteristic Functions, Scattering Functions and Transfer Functions
Editors	Daniel Alpay, Victor Vinnikov
Publisher	Springer International Publishing
Pages	149-179
Number of pages	31
ISBN (Print)	9783034601825
DOIs	https://doi.org/10.1007/978-3-0346-0183-2_8
State	Published - 2010
Event	International Conference on Characteristic functions and transfer functions in operator theory and system theory, 2007 - Beersheba, Israel Duration: 9 Jul 2007 → 13 Jul 2007

Publication series

Name	Operator Theory: Advances and Applications
Volume	197
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Conference

Conference	International Conference on Characteristic functions and transfer functions in operator theory and system theory, 2007
Country/Territory	Israel
City	Beersheba
Period	9/07/07 → 13/07/07

Bibliographical note

Publisher Copyright:
© 2009 Birkhäuser Verlag Basel/Switzerland.

Keywords

Connectedness
Convexity
Numerical range
Quadratic forms
Toeplitz-Hausdorff Theorem

Access to Document

10.1007/978-3-0346-0183-2_8

Cite this

Feldman, I., Krupnik, N., & Markus, A. (2010). Convexity of ranges and connectedness of level sets of quadratic forms. In D. Alpay, & V. Vinnikov (Eds.), Characteristic Functions, Scattering Functions and Transfer Functions (pp. 149-179). (Operator Theory: Advances and Applications; Vol. 197). Springer International Publishing. https://doi.org/10.1007/978-3-0346-0183-2_8

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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.",

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",

doi = "10.1007/978-3-0346-0183-2\_8",

language = "אנגלית",

isbn = "9783034601825",

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publisher = "Springer International Publishing",

pages = "149--179",

editor = "Daniel Alpay and Victor Vinnikov",

booktitle = "Characteristic Functions, Scattering Functions and Transfer Functions",

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Feldman, I, Krupnik, N & Markus, A 2010, Convexity of ranges and connectedness of level sets of quadratic forms. in D Alpay & V Vinnikov (eds), Characteristic Functions, Scattering Functions and Transfer Functions. Operator Theory: Advances and Applications, vol. 197, Springer International Publishing, pp. 149-179, International Conference on Characteristic functions and transfer functions in operator theory and system theory, 2007, Beersheba, Israel, 9/07/07. https://doi.org/10.1007/978-3-0346-0183-2_8

Convexity of ranges and connectedness of level sets of quadratic forms. / Feldman, I.; Krupnik, N.; Markus, A.
Characteristic Functions, Scattering Functions and Transfer Functions. ed. / Daniel Alpay; Victor Vinnikov. Springer International Publishing, 2010. p. 149-179 (Operator Theory: Advances and Applications; Vol. 197).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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KW - Connectedness

KW - Convexity

KW - Numerical range

KW - Quadratic forms

KW - Toeplitz-Hausdorff Theorem

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Convexity of ranges and connectedness of level sets of quadratic forms

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

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Cite this