On Two-Parameter Regularized Semigroups and the Cauchy Problem | Zendy

Mohammad Janfada | Zendy

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On Two-Parameter Regularized Semigroups and the Cauchy Problem

Author(s) -

Mohammad Janfada

Publication year - 2009

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2009/415847

Subject(s) - mathematics , semigroup , uniqueness , banach space , bounded function , injective function , cauchy problem , pure mathematics , bounded operator , operator (biology) , cauchy distribution , initial value problem , linear operators , space (punctuation) , mathematical analysis , biochemistry , chemistry , repressor , transcription factor , gene , linguistics , philosophy

Suppose that is a Banach space and is aninjective operator in (), the space of all bounded linearoperators on . In this note, a two-parameter -semigroup(regularized semigroup) of operators is introduced, and some of itsproperties are discussed. As an application we show that theexistence and uniqueness of solution of the 2-abstract Cauchyproblem (/())(1,2)=(1,2),=1,2, >0, (0,0)=, ∈((1)∩(2)) is closely related to the two-parameter -semigroups ofoperators

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