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A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L a2 (ℝ+;ma(x)dx)

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Abstract

Pseudo-differential operators (PDO) \(Q(x,{{\cal L}_{a,x}})\) and \({\cal Q}(x,{{\cal L}_{a,x}})\) involving the index Whittaker transform are defined. Estimates for these operators in Hilbert space L a2 (ℝ+;ma(x)dx) are obtained. A symbol class Ω is introduced. Later product and commutators for the PDO are investigated and their boundedness results are discussed.

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Acknowledgements

Authors are very thankful to the reviewers for their constructive comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India

    Jeetendrasingh Maan & Akhilesh Prasad

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  1. Jeetendrasingh Maan
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  2. Akhilesh Prasad
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Correspondence to Akhilesh Prasad.

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Conflict of Interest The authors declare no conflict of interest.

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Second author was supported by Science and Engineering Research Board, Government of India, under Grant No. EMR/2016/005141

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Maan, J., Prasad, A. A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L a2 (ℝ+;ma(x)dx). Acta. Math. Sin.-English Ser. (2024). https://doi.org/10.1007/s10114-024-3162-6

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  • DOI: https://doi.org/10.1007/s10114-024-3162-6

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