About this book
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.
47L60,46N30,46N50,42C15,65R10. positive definite functions unitary representations spectral theory Pontryagin-Bochner duality reproducing kernel Hilbert space completely monotone functions Gaussian processes Gelfand-triple Unbounded operators von Neumann’s theory of deficiency indices
- DOI https://doi.org/10.1007/978-3-319-39780-1
- Copyright Information Springer International Publishing Switzerland 2016
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-39779-5
- Online ISBN 978-3-319-39780-1
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
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