Positive definite and definitizable functions
By: Zoltán Sasvári.
Edition: 1st ed.
Series: Mathematical topics ;
Publisher: Akademie Verlag; VCH
Published: 1994
Place of publication: Berlin; New York
Language: eng
Number of pages: 206
Subjects: Positive-definite functions.
Notes: Includes bibliographical references (p. [190]-202) and index.
Table of contents: title: 1. Positive definite functions.; title: 1.1. Notation and preliminaries.; title: 1.2. Inner product spaces defined by complex-valued functions.; title: 1.3. Construction of the Hilbert space H(f).; title: 1.4. Some inequalities.; title: 1.5. Convergence of positive definite functions.; title: 1.6. Convolution and positive definite functions.; title: 1.7. Integrally positive definite functions.; title: 1.8. Extremal positive definite functions and irreducible representations.; title: 1.9. Bochner's theorem.; title: 1.10. Examples of positive definite functions --; title: 2. Some applications of positive definite functions.; title: 2.1. Duality of abelian groups.; title: 2.2. Spectral decomposition of unitary representations of abelian groups.; title: 2.3. Unitary representations of compact groups --; title: 3. Decomposition of positive definite functions.; title: 3.1. Decomposition of measurable positive definite functions.; title: 3.2. Decomposition of arbitrary positive definite functions.; title: 3.3. A finer decomposition.; title: 3.4. Equivalence of local and global measurability --; title: 4. Extension of positive definite functions.; title: 4.1. Extension from symmetric sets.; title: 4.2. The one dimensional case.; title: 4.3. The multidimensional case.; title: 4.4. Extension from subgroups --; title: 5. Functions with a finite number of negative squares.; title: 5.1. Definition and connection with unitary representations in Pontryagin spaces.; title: 5.2. Characterization of bounded functions with [kappa] negative squares.; title: 5.3. Measurable functions with [kappa] negative squares.; title: 5.4. Functions of finite rank.; title: 5.5. Definitizability of functions with [kappa] negative squares --; title: 6. Definitizable functions.; title: 6.1. Definition and some simple properties.; title: 6.2. The singularities of definitizable functions.; title: 6.3. Functions of finite order.; title: 6.4. Integral representation of functions [actual symbol not reproducible].; title: 6.5. Further results.; title: 6.6. The singularities of a function with [kappa] negative squares --; title: App. A Pontryagin spaces --; title: App. B Invariant subspaces of unitary operators in Pontryagin spaces.