Functional Calculus for the Series of Semigroup Generators Via Transference

Shawgy Hussein; Simon Joseph; Ahmed Sufyan; Murtada Amin; Ranya Tahir; Hala Taha

Functional Calculus for the Series of Semigroup Generators Via Transference

Shawgy Hussein * §

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Ahmed Sufyan

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Murtada Amin

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Ranya Tahir

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Hala Taha

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§ Upper Nile University

Functional Calculus for the Series of Semigroup Generators Via Transference

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Abstract

In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved thatif -𝐴𝐴 𝑗𝑗 be the sequence generates 𝐶𝐶 0 -semigroups on a Hilbert space, then for each 𝜀𝜀 > -1 the sequence of operators 𝐴𝐴 𝑗𝑗 has bounded calculus for the closed ideal of bounded holomorphic functions on right half-plane. The bounded of this calculus grows at most logarithmically as(1 + 𝜀𝜀) ↘ 0. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a socalled (strong) m-bounded calculus for all m ∈ ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called 𝛾𝛾 𝑗𝑗 -𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 semigroups, the Hilbert space results actually hold in general Banach spaces.

References

11 Cites in Article

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Shawgy Hussein, Ahmed Sufyan, Murtada Amin, Ranya Tahir, Hala Taha. 2019. "Functional Calculus for the Series of Semigroup Generators Via Transference". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 19 (GJSFR Volume 19 Issue F5).

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GJSFR Volume 19 Issue F5

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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Classification

GJSFR-F Classification MSC 2010: 47A60

Submission ReceivedNovember 14, 2019
Peer Review Double Blind
Handling Editor
Accepted December 5, 2019
Published December 15, 2019

Version of record

v1.2

Issue date

December 23, 2019

Language

English

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Article Matrices

Total Score: 120

Country: Sudan

Subject: Global Journal of Science Frontier Research

Authors: Shawgy Hussein, Simon Joseph, Ahmed Sufyan, Murtada Amin, Ranya Tahir, Hala Taha (PhD/Dr. count: 0)

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