Unified speed estimation of various stabilities

Mu-Fa Chen

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 9-12
  • ISSN: 2300-7451

Abstract

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The main topic of this talk is the speed estimation of stability/instability. The word “various” comes with no surprising since there are a lot of different types of stability/instability and each of them has its own natural distance to measure. However, the adjective “unified” is very much unexpected. The talk surveys our recent progress on the topic, made in the past five years or so.

How to cite

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Mu-Fa Chen. "Unified speed estimation of various stabilities." Special Matrices 4.1 (2016): 9-12. <http://eudml.org/doc/276914>.

@article{Mu2016,
abstract = {The main topic of this talk is the speed estimation of stability/instability. The word “various” comes with no surprising since there are a lot of different types of stability/instability and each of them has its own natural distance to measure. However, the adjective “unified” is very much unexpected. The talk surveys our recent progress on the topic, made in the past five years or so.},
author = {Mu-Fa Chen},
journal = {Special Matrices},
language = {eng},
number = {1},
pages = {9-12},
title = {Unified speed estimation of various stabilities},
url = {http://eudml.org/doc/276914},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Mu-Fa Chen
TI - Unified speed estimation of various stabilities
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 9
EP - 12
AB - The main topic of this talk is the speed estimation of stability/instability. The word “various” comes with no surprising since there are a lot of different types of stability/instability and each of them has its own natural distance to measure. However, the adjective “unified” is very much unexpected. The talk surveys our recent progress on the topic, made in the past five years or so.
LA - eng
UR - http://eudml.org/doc/276914
ER -

References

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  1. [1] Chen, M.F. (2003). Variational formulas of Poincaré-type inequalities for birth-death processes. Acta Math. Sin. Eng. Ser. 19(4): 625-644.[Crossref] Zbl1040.60064
  2. [2] Chen, M.F. (2004). From Markov Chains to Non-equilibrium Particle Systems. World Scientific. 2nd ed. (1st ed., 1992). 
  3. [3] Chen, M.F. (2005). Eigenvalues, Inequalities, and Ergodic Theory. Springer, London. Zbl1079.60005
  4. [4] Chen, M.F. (2007). Exponential convergence rate in entropy. Front. Math. China, 2(3): 329–358.[Crossref] Zbl1152.60059
  5. [5] Chen M.F. (2010). Speed of stability for birth–death processes. Front Math China 5(3): 379–515. 
  6. [6] Chen, M.F. (2012). Lower bounds of principal eigenvalue in dimension one. Front. Math. China 7(4): 645–668.[WoS][Crossref] Zbl1263.34122
  7. [7] Chen, M.F. (2013a). Bilateral Hardy-type inequalities. Acta Math Sin Eng Ser. 29(1): 1–32.[Crossref] Zbl1263.26028
  8. [8] Chen, M.F. (2013b). Bilateral Hardy-type inequalities and application to geometry. Mathmedia 37(2): 12–32; Math. Bulletin 52(8/9) (in Chinese). 
  9. [9] Chen, M.F. (2014). Criteria for discrete spectrum of 1D operators. Commu. Math. Stat. 2: 279–309[Crossref] Zbl1309.47005
  10. [10] Chen, M.F. (2015a). Criteria for two spectral problems of 1D operators (in Chinese). Sci Sin Math, 44(1): 
  11. [11] Chen, M.F. (2015b). The optimal constant in Hardy-type inequalities. Acta Math. Sinica, Eng. Ser.[Crossref][WoS] Zbl1318.26035
  12. [12] Chen, M.F. (2015c). Progress on Hardy-type inequalities. Chapter 6 in the book “Festschrift Masatoshi Fukushima”, eds: Z.Q. Chen, N. Jacob, M. Takeda, and T. Uemura, World Sci. Zbl1341.42012
  13. [13] Chen, M.F. and Zhang, X. (2014) Isospectral operators. Commu Math Stat 2: 17–32.[Crossref] Zbl1310.47047
  14. [14] Liao, Z.W. (2015). Discrete weighted Hardy inequalities with different boundary conditions. arXiv:1508.04601. 

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