Embedding of Semigroups of Lipschitz Maps into Positive Linear Semigroups on Ordered Banach Spaces Generated by Measures

被引：29
作者：
Hille, Sander C. [1 ]
Worm, Daniel T. H. [1 ]
机构：
[1] Leiden Univ, Math Inst, NL-2300 RA Leiden, Netherlands
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2009年 / 63卷 / 03期
关键词：
Nonlinear semigroups; metric spaces; Lipschitz functions; finite measures; CHEMOTAXIS; EQUATIONS; MODELS;
D O I：
10.1007/s00020-008-1652-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Interpretation, derivation and application of a variation of constants formula for measure-valued functions motivate our investigation of properties of particular Banach spaces of Lipschitz functions on a metric space and semigroups defined on their (pre) duals. Spaces of measures densely embed into these preduals. The metric space embeds continuously in these preduals, even isometrically in a specific case. Under mild conditions, a semigroup of Lipschitz transformations on the metric space then embeds into a strongly continuous semigroups of positive linear operators on these Banach spaces generated by measures.
引用
收藏
页码：351 / 371
页数：21
相关论文
共 22 条
[1]  
Arens R.F., 1956, Pacific J. Math., V6, P397
[2]   Model hierarchies for cell aggregation by chemotaxis [J].
Chalub, Fabio ;
Dolak-Struss, Yasmin ;
Markowich, Peter ;
Oelz, Dietmar ;
Schmeiser, Christian ;
Soreff, Alexander .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2006, 16 (07) :1173-1197
[3]   Kinetic models for chemotaxis and their drift-diffusion limits [J].
Chalub, FACC ;
Markowich, PA ;
Perthame, B ;
Schmeiser, C .
MONATSHEFTE FUR MATHEMATIK, 2004, 142 (1-2) :123-141
[4]  
CONWAY J, 1990, COURSE FUNCTIONAL AN
[5]  
DIEKMANN O., 1993, AMR9305 CWI
[6]  
Diestel J., 1977, Vector Measures, Mathematical surveys and monographs, V15
[7]   CONVERGENCE OF BAIRE MEASURES [J].
DUDLEY, RM .
STUDIA MATHEMATICA, 1966, 27 (03) :251-&
[8]  
DUDLEY RM, 1974, STUD MATH, V51, P275
[9]   A BRANCHING RANDOM EVOLUTION AND A NONLINEAR HYPERBOLIC EQUATION [J].
DUNBAR, SR .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1988, 48 (06) :1510-1526
[10]  
ENGEL KJ, 2000, ONE PARAMETER SEMIGR
123