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Extensions of Positive Definite Functions

Applications and Their Harmonic Analysis

  • Palle Jorgensen
  • Steen Pedersen
  • Feng Tian

Part of the Lecture Notes in Mathematics book series (LNM, volume 2160)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 1-16
  3. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 17-46
  4. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 47-66
  5. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 67-92
  6. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 93-113
  7. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 115-150
  8. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 151-169
  9. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 171-191
  10. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 193-195
  11. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 197-216
  12. Palle Jorgensen, Steen Pedersen, Feng Tian
    Pages 217-218
  13. Back Matter
    Pages 219-233

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Palle Jorgensen
    • 1
  • Steen Pedersen
    • 2
  • Feng Tian
    • 3
  1. 1.Department of MathematicsThe University of Iowa Iowa CityUSA
  2. 2.Department of MathematicsWright State University DaytonUSA
  3. 3.Department of MathematicsHampton University HamptonUSA

Bibliographic information

  • 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
  • Buy this book on publisher's site
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