An edition of Positive definite and definitizable functions
(1994)
Positive definite and definitizable functions
1st ed.
by Zoltán Sasvári
- 1 Want to read
Share
×Close
Provides an introduction to the theory of positive definite and definitzable functions on groups. Chapters 1-4 deal with positive definite functions and their applications while chapters 5-6 are devoted to functions with a finite number of negative squares and to definitizable functions.
Check nearby libraries
Buy this book
| Edition | Availability |
|---|---|
1
Positive definite and definitizable functions
1994, Akademie Verlag, VCH
in English
- 1st ed.
3055014464 9783055014468
|
aaaa
|
Book Details
Table of Contents
1. Positive definite functions.
1.1. Notation and preliminaries.
1.2. Inner product spaces defined by complex-valued functions.
1.3. Construction of the Hilbert space H(f).
1.4. Some inequalities.
1.5. Convergence of positive definite functions.
1.6. Convolution and positive definite functions.
1.7. Integrally positive definite functions.
1.8. Extremal positive definite functions and irreducible representations.
1.9. Bochner's theorem.
1.10. Examples of positive definite functions --
2. Some applications of positive definite functions.
2.1. Duality of abelian groups.
2.2. Spectral decomposition of unitary representations of abelian groups.
2.3. Unitary representations of compact groups --
3. Decomposition of positive definite functions.
3.1. Decomposition of measurable positive definite functions.
3.2. Decomposition of arbitrary positive definite functions.
3.3. A finer decomposition.
3.4. Equivalence of local and global measurability --
4. Extension of positive definite functions.
4.1. Extension from symmetric sets.
4.2. The one dimensional case.
4.3. The multidimensional case.
4.4. Extension from subgroups --
5. Functions with a finite number of negative squares.
5.1. Definition and connection with unitary representations in Pontryagin spaces.
5.2. Characterization of bounded functions with [kappa] negative squares.
5.3. Measurable functions with [kappa] negative squares.
5.4. Functions of finite rank.
5.5. Definitizability of functions with [kappa] negative squares --
6. Definitizable functions.
6.1. Definition and some simple properties.
6.2. The singularities of definitizable functions.
6.3. Functions of finite order.
6.4. Integral representation of functions [actual symbol not reproducible].
6.5. Further results.
6.6. The singularities of a function with [kappa] negative squares --
App. A Pontryagin spaces --
App. B Invariant subspaces of unitary operators in Pontryagin spaces.
Edition Notes
Includes bibliographical references (p. [190]-202) and index.
Classifications
The Physical Object
Edition Identifiers
Work Identifiers
Links outside Open Library
Community Reviews (0)
Lists
See All
| October 18, 2022 | Edited by ImportBot | import existing book |
| February 28, 2020 | Edited by Kaustubh Chakraborty | Added description |
| February 28, 2020 | Edited by Kaustubh Chakraborty | Added new cover |
| February 28, 2020 | Edited by Kaustubh Chakraborty | Edited tags |
| December 10, 2009 | Created by WorkBot | add works page |