Extensions of Positive Definite Functions
Applications and Their Harmonic Analysis
Published on 8. July 2016
XXVI, 231 pages
978-3-319-39780-1 (ISBN)
Description
This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed group. It is therefore both an art and a science to produce solid conclusions from restricted or limited data.
While the theory of is important in many areas of pure and applied mathematics, it is difficult for students and for the novice to the field, to find accessible presentations which cover all relevant points of view, as well as stressing common ideas and interconnections. We have aimed at filling this gap, and we have stressed hands-on-examples.
While the theory of is important in many areas of pure and applied mathematics, it is difficult for students and for the novice to the field, to find accessible presentations which cover all relevant points of view, as well as stressing common ideas and interconnections. We have aimed at filling this gap, and we have stressed hands-on-examples.
More details
Series
Edition
1st ed. 2016
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
XXVI, 231 p. 48 illus., 9 illus. in color.
File size
3,74 MB
ISBN-13
978-3-319-39780-1 (9783319397801)
DOI
10.1007/978-3-319-39780-1
Schweitzer Classification
Other editions
Additional editions
Palle Jorgensen | Steen Pedersen | Feng Tian
Extensions of Positive Definite Functions
Applications and Their Harmonic Analysis
Book
07/2016
Springer
€53.49
Shipment within 10-15 days
Content
Introduction.-Extensions of Continuous Positive Definite Functions.-The Case of More General Groups.-Examples.-Type I vs. Type II Extensions.-Spectral Theory for Mercer Operators, and Implications for Ext (F).-Green's Functions.-Comparing the Different RKHSs HF and HK.-Comparing the Different RKHSs HF and HK.-Models for, and Spectral Representations of, Operator Extensions.-Overview and Open Questions.-List of Figures.-List of Tables.-References.-Index.
