"Structure Of Fractional Spaces Generated
By The Positive Operators"




Prof. Allaberen Ashyralyev

(Fatih University)



Abstract: It is a well-known that the study of the various properties of PDE is based on a positivity property of the differential operator in a Banach space.The positivity of the wider class of differential operators have been studied by Yosida,K. (Japan), Kato T.(USA),Agman S. (Israel), Friedman A.(USA), Solomyak M.Z.(USSR), Sobolevskii P.E. (USSR), Stewart H.B.(USA) and et al. Important progress has been made in the study of positive operators from the viewpoint of the stability analysis of high order accuracy difference schemes for PDE. The application of theory of fractional spaces generated by the positive operators in a Banach Space permit us to investigate the stability and coercive stability properties of difference schemes in various norms for PDE specially when we can not able to use of a maximum principle and energy method. In the present paper we study the structure of fractional spaces generated by the positive differential and difference operators. The known facts, new results and open problems are presented.




Tea and cookies will be served before the seminar.




Date:  Thursday, March 29, 2007

Time: 14.40

Place: Mathematics Seminar Room, SA-141