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Notions of Positivity and the Geometry of Polynomials

  • Book
  • © 2011

Overview

Editors:
  1. Petter Brändén

    1. , Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

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  2. Mikael Passare

    1. , Mathematical Department, Stockholm University, Stockholm, Sweden

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    You can also search for this editor in PubMed   Google Scholar

  3. Mihai Putinar

    1. , Department of Mathematics, University of California, Santa Barbara, USA

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  • At the interface between positivity and the geometry, combinatorics or analysis of polynomials of one or several variables solicited articles from a select group of mathematicians and physicists dedicated to the memory of Julius Borcea (1968-2009), a distinguished mathematician
  • Includes supplementary material: sn.pub/extras

Part of the book series: Trends in Mathematics (TM)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Commuting Linear Differential Operators and Hankel Matrices

    • Alexandru Aleman, Andreea Sarafoleanu
    Pages 1-15

  3. Variants of the Effective Nullstellensatz and Residue Calculus

    • Mats Andersson, Elizabeth Wulcan
    Pages 17-31

  4. An Extension Problem for Convex Functions

    • Bo Berndtsson
    Pages 33-37

  5. Subharmonic Configurations and Algebraic Cauchy Transforms of Probability Measures

    • Jan-Erik Björk, Julius Borcea, Rikard Bøgvad
    Pages 39-62

  6. Proof of the Monotone Column Permanent Conjecture

    • Petter Brändén, James Haglund, Mirkó Visontai, David G. Wagner
    Pages 63-78

  7. Tracial Nullstellensätze

    • Matej Brešar, Igor Klep
    Pages 79-101

  8. Iterated Turán Inequalities and a Conjecture of P. Brändén

    • George Csordas
    Pages 103-113

  9. Double Scaling Limit for Modified Jacobi-Angelesco Polynomials

    • Klaas Deschout, Arno B. J. Kuijlaars
    Pages 115-161

  10. Constrained Approximation via Functional Analysis

    • Peter Duren, Harold S. Shapiro
    Pages 163-166

  11. An Elementary Proof of the B. and M. Shapiro Conjecture for Rational Functions

    • Alexandre Eremenko, Andrei Gabrielov
    Pages 167-178

  12. The Pressure, Densities and First-order Phase Transitions Associated with Multidimensional SOFT

    • Shmuel Friedland, Uri N. Peled
    Pages 179-220

  13. Matrix Weyl Functions and Non-Abelian Coxeter-Toda Lattices

    • Michael Gekhtman, Olena Korovnichenko
    Pages 221-237

  14. On the Exponential Transform of Lemniscates

    • Björn Gustafsson, Vladimir Tkachev
    Pages 239-257

  15. On a Family of Positive Linear Integral Operators

    • Mourad Ismail, Plamen Simeonov
    Pages 259-274

  16. Monomial Inequalities for Newton Coefficients and Determinantal Inequalities for p-Newton Matrices

    • C. R. Johnson, C. Marijuán, M. Pisonero, O. Walch
    Pages 275-282

  17. Borcea’s Variance Conjectures on the Critical Points of Polynomials

    • Dmitry Khavinson, Rajesh Pereira, Mihai Putinar, Edward B. Saff, Serguei Shimorin
    Pages 283-309

  18. Stability on {0, 1, 2, …}S: Birth-Death Chains and Particle Systems

    • Thomas M. Liggett, Alexander Vandenberg-Rodes
    Pages 311-329

  19. The Convex Hull of a Variety

    • Kristian Ranestad, Bernd Sturmfels
    Pages 331-344

  20. Blenders

    • Bruce Reznick
    Pages 345-373
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Keywords

About this book

The book consists of solicited articles from a select group of mathematicians and physicists working at the interface between positivity and the geometry, combinatorics or analysis of polynomials of one or several variables. It is dedicated to the memory of Julius Borcea (1968-2009), a distinguished mathematician, Professor at the University of Stockholm. With his extremely original contributions and broad vision, his impact on the topics of the planned volume cannot be underestimated. All contributors knew or have exchanged ideas with Dr. Borcea, and their articles reflect, at least partially, his heritage.

Editors and Affiliations

  • , Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

    Petter Brändén

  • , Mathematical Department, Stockholm University, Stockholm, Sweden

    Mikael Passare

  • , Department of Mathematics, University of California, Santa Barbara, USA

    Mihai Putinar

Bibliographic Information

  • Book Title: Notions of Positivity and the Geometry of Polynomials

  • Editors: Petter Brändén, Mikael Passare, Mihai Putinar

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-0142-3

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Basel AG 2011

  • Hardcover ISBN: 978-3-0348-0141-6Published: 02 September 2011

  • Softcover ISBN: 978-3-0348-0344-1Published: 27 November 2013

  • eBook ISBN: 978-3-0348-0142-3Published: 01 September 2011

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: XX, 404

  • Topics: Analysis

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