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Factorization of the Hilbert Matrix Based on Cesàro and Gamma Matrices

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Abstract

In this paper, we introduce a factorization for the infinite Hilbert matrix based on Cesàro matrices. Moreover, through the relation between Cesàro and Gamma matrices, we extract our second factorization for the Hilbert matrix based on Gamma matrices. The results of these factorizations are two new inequalities one of which is a generalized version of the well-known Hilbert’s inequality.

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Acknowledgements

The author would like to express his gratitude to the referee for several corrections and improvements to the results.

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  1. Young Researchers and Elite Club, Marvdasht Branch, Izlamic Azad University, Marvdasht, Iran

    H. Roopaei

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  1. H. Roopaei
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Correspondence to H. Roopaei.

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Dedicated to Prof. Maryam Mirzakhani who in spite of a short lifetime, left a long standing impact on mathematics.

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Roopaei, H. Factorization of the Hilbert Matrix Based on Cesàro and Gamma Matrices. Results Math 75, 3 (2020). https://doi.org/10.1007/s00025-019-1129-1

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  • DOI: https://doi.org/10.1007/s00025-019-1129-1

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