Optimal polynomial decay of functions and operator semigroups

被引：499

作者：

Borichev, Alexander ^{[2
]}

Tomilov, Yuri ^{[1
,3
]}

机构：

[1] Nicholas Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland

[2] Univ Aix Marseille 1, Ctr Math & Informat, F-13453 Marseille, France

[3] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland

来源：

MATHEMATISCHE ANNALEN | 2010年 / 347卷 / 02期

关键词：

LOCAL ENERGY DECAY; TAUBERIAN-THEOREMS; WAVE-EQUATIONS; STABILITY;

D O I：

10.1007/s00208-009-0439-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize the polynomial decay of orbits of Hilbert space C-0-semigroups in resolvent terms. We also show that results of the same type for general Banach space semigroups and functions obtained recently in Batty and Duyckaerts (J Evol Eq 8: 765-780, 2008) are sharp. This settles a conjecture posed in Batty and Duyckaerts (2008).

引用

页码：455 / 478

页数：24

共 27 条

[1] TAUBERIAN-THEOREMS AND STABILITY OF ONE-PARAMETER SEMIGROUPS
ARENDT, W
BATTY, CJK
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 306 (02) : 837 - 852
[2] Arendt W., 2001, Monographs in Mathematics, V96
[3] Polynomial stability of operator semigroups
Batkai, Andras
Engel, Klaus-Jochen
Pruess, Jan
Schnaubelt, Roland
[J]. MATHEMATISCHE NACHRICHTEN, 2006, 279 (13-14) : 1425 - 1440
[4] Non-uniform stability for bounded semi-groups on Banach spaces
Batty, Charles J. K.
Duyckaerts, Thomas
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2008, 8 (04) : 765 - 780
[5] TAUBERIAN-THEOREMS FOR THE LAPLACE-STIELTJES TRANSFORM
BATTY, CJK
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 322 (02) : 783 - 804
[6] BATTY CJK, 1994, FUNCTIONAL ANAL OPER, V30, P35
[7] Local energy decay of the wave equation for the exterior problem and absence of resonance in the neighborhood of the real axis
Burq, N
[J]. ACTA MATHEMATICA, 1998, 180 (01) : 1 - 29
[8] Burq N, 2007, MATH RES LETT, V14, P35
[9] Stability of C0-semigroups and geometry of Banach spaces
Chill, R
Tomilov, Y
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2003, 135 : 493 - 511
[10] Stability of operator semigroups: Ideas and results
Chill, Ralph
Tomilov, Yuri
[J]. PERSPECTIVES IN OPERATOR THEORY, 2007, 75 : 71 - 109

← 1 2 3 →