Skip to main content

L1 minimization in one and several variables

Part II: Characterization Theorems

  • 276 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 479)

Keywords

  • Null Space
  • Minimal Support
  • Linear Differential Operator
  • Extremal Measure
  • Minimal Total Variation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. D. Fisher and J. W. Jerome, “Spline solutions to L1 extremal problems in one and several variables”, J. Approximation Theory, 13 (1975), 73–83.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. A. Gleason, Fundamentals of Abstract Analysis Addison-Wesley, Reading, Mass., 1966.

    MATH  Google Scholar 

  3. R. B. Holmes, “R-splines in Banach spaces: I”, J. Math. Anal. Appl., 40 (1972), 574–593.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. A. Ioffe and V. Tihomirov, “Extension of variational problems”, Trans. Moscow Math. Soc., 18 (1968), 207–273.

    MathSciNet  Google Scholar 

  5. O. L. Mangasarian and L. L. Schumaker, “Discrete splines via mathematical programming”, SIAM J. Control, 9 (1971), 174–183.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. I. Singer, “Dea Mai Buna Approximare in Spatii Vectoriale Normate prin Elementa din Subspatii Vectoriale”, Editura Acad. Republ. Social, Romania, Bucuresti, 1967.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1975 Springer-Verlag

About this chapter

Cite this chapter

Fisher, S.D., Jerome, J.W. (1975). L1 minimization in one and several variables. In: Minimum Norm Extremals in Function Spaces. Lecture Notes in Mathematics, vol 479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097065

Download citation

  • DOI: https://doi.org/10.1007/BFb0097065

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07394-9

  • Online ISBN: 978-3-540-37599-9

  • eBook Packages: Springer Book Archive