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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 2
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Articles

S-operators related to a finite measure space

Pages 326-339 | Received 22 Dec 2017, Accepted 19 Jun 2018, Published online: 10 Jul 2018
 

ABSTRACT

In this work we introduce and study a class of linear operators related to a finite measure space, for which its L2-Hilbert space is separable. These linear operators represent a generalization of pseudo-differential operators on S1, where S1 is the unit circle with centre at the origin. We call these operators, S-operators or generalized pseudo-differential operators on S, where (S,B,m) is the corresponding finite measure space for which the L2-space is separable. We give some L2-boundedness and compactness results, and we also study the Hilbert–Schmidt property in connection with this class of linear operators. In the end we give some examples of finite measure spaces and corresponding S-operators for which we can apply our results.

2010 MSC SUBJECT CLASSIFICATIONS:

Acknowledgements

The author is grateful to the anonymous referee for valuable remarks and comments which led to several improvements of the original paper.

Disclosure statement

No potential conflict of interest was reported by the author.

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