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3 results

Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities
  • Rupert L. Frank, Ari Laptev, Timo Weidl
  • Published online:
    03 November 2022
    Print publication:
    17 November 2022
  • The analysis of eigenvalues of Laplace and Schrödinger operators is an important and classical topic in mathematical physics with many applications. This book presents a thorough introduction to the area, suitable for masters and graduate students, and includes an ample amount of background material on the spectral theory of linear operators in Hilbert spaces and on Sobolev space theory. Of particular interest is a family of inequalities by Lieb and Thirring on eigenvalues of Schrödinger operators, which they used in their proof of stability of matter. The final part of this book is devoted to the active research on sharp constants in these inequalities and contains state-of-the-art results, serving as a reference for experts and as a starting point for further research.

  • SHARP CONSTANTS BETWEEN EQUIVALENT NORMS IN WEIGHTED LORENTZ SPACES

  • Part of
  • SORINA BARZA, JAVIER SORIA
  • Journal:
    Journal of the Australian Mathematical Society / Volume 88 / Issue 1 / February 2010
    Published online by Cambridge University Press:
    22 January 2010, pp. 19-27
    Print publication:
    February 2010
    • Article
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  • For an increasing weight w in Bp (or equivalently in Ap), we find the best constants for the inequalities relating the standard norm in the weighted Lorentz space Λp(w) and the dual norm.