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Hypercontractivity in group Von Neumann algebras / Marius Junge...[et al.]

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 249, no 1183.Publication details: Providence : American Mathematical Society, 2017.Description: xii, 83 pages ; 26 cmISBN:
  • 9781470425654 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. The combinatorial method -- 2. Optimal time estimates -- 3. Poisson-like lengths -- Appendix A. Logarithmic Sobolev inequalities -- Appendix B. The word length in $\mathbb {Z}_n$ -- Appendix C. Numerical analysis -- Appendix D. Technical inequalities -- Bibliography.
Summary: Provides a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. The authors illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive $L_2 \to L_q$ inequalities with respect to the Markov process given by the word length and with $q$ an even integer.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 138225
Total holds: 0

Includes bibliographical references.

1. The combinatorial method --
2. Optimal time estimates --
3. Poisson-like lengths --
Appendix A. Logarithmic Sobolev inequalities --
Appendix B. The word length in $\mathbb {Z}_n$ --
Appendix C. Numerical analysis --
Appendix D. Technical inequalities --
Bibliography.

Provides a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. The authors illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive $L_2 \to L_q$ inequalities with respect to the Markov process given by the word length and with $q$ an even integer.

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