ISSN:0024-6115    

DOI:10.1112/plms/s3-54.2.193

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-54.2.216

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-54.2.247

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-54.2.267

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

This paper is concerned with the relationship between ordinary linear quasi‐differential expressions, defined in terms of locally Lebesgue integrable coefficients given on an interval of the real line, and the ‘classical’ differential expressions with smooth (differentiable to certain prescribed orders) coefficients. The results give necessary and sufficient conditions for the general quasi‐differential expression to be equivalent to a classical expression. In an appropriate sense the results can be considered as best possible. Examples of the results are given for second‐order and third‐order differential expressions.

ISSN:0024-6115    

DOI:10.1112/plms/s3-54.2.300

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Resolvent positive operators on an ordered Banach space (with generating and normal positive cone) are by definition linear (possibly unbounded) operators whose resolvent exists and is positive on a right half‐line. Even though these operators are defined by a simple (purely algebraic) condition, analogues of the basic results of the theory ofC0‐semigroups can be proved for them. In fact, ifAis resolvent positive and has a dense domain, then the Cauchy problem associated withAhas a unique solution for every initial value in the domain ofA2, and the solution is positive if the initial value is positive. Also the converse is true (if we assume thatAhas a non‐empty resolvent set andD(A2)∩E+is dense inE+). Moreover, every positive resolvent is a Laplace–‐Stieltjes transform of a so‐called integrated semigroup; and conversely every such (increasing, non‐degenerate) integrated semigroup defines a unique resolvent positive operator.

ISSN:0024-6115    

DOI:10.1112/plms/s3-54.2.321

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-54.2.350

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-54.2.367

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/j.1460-244X.1987.tb00439.x

出版商:Oxford University Press    

年代:1987

数据来源: WILEY