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A note on fractional powers of strongly positive operators and their applications

  • Allaberen Ashyralyev EMAIL logo and Ayman Hamad
Published/Copyright: May 11, 2019

Abstract

The present paper deals with fractional powers of positive operators in a Banach space. The main theorem concerns the structure of fractional powers of positive operators in fractional spaces. As applications, the structure of fractional powers of elliptic operators is studied.


Dedicated in memory of Prof. Pavel Evseevich Sobolevskii


Acknowledgements

This project was conducted with the support of the “RUDN University Program 5-100” and published under target program BR05236656 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan. Finally, some of statements of the present paper were formulated in [7] without proof. The authors are grateful to Prof. Virgina Kiryakova and referee of this paper for the useful comments and relevant references.

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Received: 2018-06-01
Published Online: 2019-05-11
Published in Print: 2019-04-24

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