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Total Positivity and Its Applications

  • Book
  • © 1996

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Editors:
  1. Mariano Gasca

    1. Department of Applied Mathematics, University of Zaragoza, Zaragoza, Spain

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  2. Charles A. Micchelli

    1. IBM, T.J. Watson Research Center, Yorktown Heights, USA

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Part of the book series: Mathematics and Its Applications (MAIA, volume 359)

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-x
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  2. Spline Functions

    1. Front Matter

      Pages 1-1
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    2. Total Positivity of the Spline Kernel and its Applications

      • Borislav Bojanov
      Pages 3-34

    3. Total Positivity Properties of LB-splines

      • Tom Lyche, Larry L. Schumaker
      Pages 35-46

    4. Total Positivity and Splines

      • Knut Mørken
      Pages 47-84

    5. Totally Positive Systems and Interpolation by Subspaces of Generalized Splines

      • Manfred Sommer, Hans Strauss
      Pages 85-94

  3. Matrix Theory

    1. Front Matter

      Pages 95-95
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    2. Preservation of Total Nonnegativity under the Hadamard Product and Related Topics

      • Jürgen Garloff, David G. Wagner
      Pages 97-102

    3. Vertex Implications for Totally Nonnegative Matrices

      • Jürgen Garloff
      Pages 103-107

    4. On Factorizations of Totally Positive Matrices

      • Mariano Gasca, Juan M. Peña
      Pages 109-130

  4. Geometric Modeling

    1. Front Matter

      Pages 131-131
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    2. Total positivity and optimal bases

      • J. M. Carnicer, J. M. Peña
      Pages 133-155

    3. Total Positivity and the Shape of Curves

      • Tim N. T. Goodman
      Pages 157-186

    4. Tchebycheff Curves

      • Marie-Laurence Mazure, Helmut Pottnann
      Pages 187-218

  6. Approximation Theory

    1. Front Matter

      Pages 275-275
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    2. Tchebycheff spaces and total positivity

      • J. M. Carnicer, J. M. Peña
      Pages 277-300
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Keywords

About this book

This volume contains both invited lectures and contributed talks presented at the meeting on Total Positivity and its Applications held at the guest house of the University of Zaragoza in Jaca, Spain, during the week of September 26-30, 1994. There were present at the meeting almost fifty researchers from fourteen countries. Their interest in thesubject of Total Positivity made for a stimulating and fruitful exchange of scientific information. Interest to participate in the meeting exceeded our expectations. Regrettably, budgetary constraints forced us to restriet the number of attendees. Professor S. Karlin, of Stanford University, who planned to attend the meeting had to cancel his participation at the last moment. Nonetheless, his almost universal spiritual presence energized and inspired all of us in Jaca. More than anyone, he influenced the content, style and quality of the presentations given at the meeting. Every article in these Proceedings (except some by Karlin hirnself) references his influential treatise Total Positivity, Volume I, Stanford University Press, 1968. Since its appearance, this book has intrigued and inspired the minds of many researchers (one of us, in his formative years, read the galley proofs and the other of us first doubted its value but then later became its totally committed disciple). All of us present at the meeting encourage Professor Karlin to return to the task of completing the anxiously awaited Volume 11 of Total Positivity.

Editors and Affiliations

  • Department of Applied Mathematics, University of Zaragoza, Zaragoza, Spain

    Mariano Gasca

  • IBM, T.J. Watson Research Center, Yorktown Heights, USA

    Charles A. Micchelli

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