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

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

1 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. We consider the question: Which subsets of X, besides S, have these properties?

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 - 1 Jan 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

Keywords

Connectedness
Convexity
Numerical range
Quadratic forms
Toeplitz-Hausdorff Theorem

ASJC Scopus subject areas

Analysis

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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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",

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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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AU - Krupnik, N.

AU - Markus, A.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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?

AB - 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?

KW - Connectedness

KW - Convexity

KW - Numerical range

KW - Quadratic forms

KW - Toeplitz-Hausdorff Theorem

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BT - Characteristic Functions, Scattering Functions and Transfer Functions

A2 - Alpay, Daniel

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PB - Springer International Publishing

T2 - International Conference on Characteristic functions and transfer functions in operator theory and system theory, 2007

Y2 - 9 July 2007 through 13 July 2007

ER -

Convexity of ranges and connectedness of level sets of quadratic forms

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

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