"Structure Of Fractional
Spaces Generated
By The Positive Operators"
By
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