Skip to main content

The One-Dimensional Truncated Moment Problem on a Bounded Interval

  • Chapter
  • First Online:
  • 3720 Accesses

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 277))

Abstract

Throughout this chapter a and b are fixed real numbers such that a < b and \(m \in \mathbb{N}\). We consider the truncated moment problem on the interval [a, b]:

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Bibliography

  1. Dette, H. and W.J. Studden: The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis, Wiley, New York, 1997.

    MATH  Google Scholar 

  2. Karlin, M. and L.S. Shapley: Geometry of Moment Spaces, Memoirs Amer. Math. Soc. 12, Providence, R. I., 1953.

    Google Scholar 

  3. Karlin, M. and W. Studden: Tchebycheff Systems: with Applications in Analysis and Statistics, Interscience, New York, 1966.

    MATH  Google Scholar 

  4. Krein, M.G.: The ideas of P.L. Cebysev and A.A. Markov in the theory of limiting values of integrals and their further developments, Uspehi Mat. Nauk 6(1951), 2–120; Amer. Math. Transl., Amer. Math. Soc., RI, 12(1951), 1–122.

    Google Scholar 

  5. Krein, M.G.: The description of all solutions of the truncated power moment problem and some problems of operator theory, Mat. Issled. 2(1967), 114–132. Amer. Mat. Soc. Transl. 95(1970), 219–234.

    Google Scholar 

  6. Krein, M.G. and A.A. Nudelman: The Markov Moment Problem and Extremal Problems, Amer. Math. Soc., Providence, R. I, 1977.

    Google Scholar 

  7. Markov, A.A.: Lectures on functions deviating least from zero, Mimeographed Notes, St. Petersburg, 1906, 244–281. Reprinted in: Selected papers on continued fractions and the theory of functions deviating least from zero, OGIZ, Moscow, 1948, 244–281. (Russian)

    Google Scholar 

  8. Schoenberg, I.J. and G. Szegö: An extremum problem for polynomials, Compositio Math. 14(1960), 260–268.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Schmüdgen, K. (2017). The One-Dimensional Truncated Moment Problem on a Bounded Interval. In: The Moment Problem. Graduate Texts in Mathematics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-319-64546-9_10

Download citation

Publish with us

Policies and ethics