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New Convolutions with Hermite Weight Functions

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Abstract

In this paper, we are working with convolutions on the positive half-line, for Lebesgue integrable functions. Six new convolutions are introduced. Factorization identities for these convolutions are derived, upon the use of Fourier sine and cosine transforms and Hermite functions. Such convolutions allow us to consider systems of convolution type equations on the half-line. Using two different methods, such systems of convolution integral equations will be analyzed. Conditions for their solvability will be considered and, under such conditions, their solutions are obtained.

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Acknowledgements

This work was supported by Fundação para a Ciência e a Tecnologia (FCT), within project UIDB/04106/2020 (CIDMA) and by national funds (OE), through FCT, I.P., in the scope of the framework contract foreseen in the numbers 4, 5, and 6 of the article 23, of the Decree-Law 57/2016, of August 29, changed by Law 57/2017, of July 19. The authors gratefully thank the Referee for the constructive comments and recommendations which definitely helped improving the readability and quality of the paper.

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Authors and Affiliations

  1. CIDMA–Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810–193, Aveiro, Portugal

    Luís Pinheiro Castro & Anabela Sousa Silva

  2. Dept. of Math., VNU University of Education, Viet Nam National University, 144 Xuan Thuy Str. Cau Giay Dist., Ha Noi, Viet Nam

    Nguyen Minh Tuan

Authors
  1. Luís Pinheiro Castro
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  2. Anabela Sousa Silva
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  3. Nguyen Minh Tuan
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Correspondence to Luís Pinheiro Castro.

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Communicated by Mahmoud Hadizade.

In honor of Professor Roland Duduchava on the occasion of his 75th birthday.

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Castro, L.P., Silva, A.S. & Tuan, N.M. New Convolutions with Hermite Weight Functions. Bull. Iran. Math. Soc. 47 (Suppl 1), 365–379 (2021). https://doi.org/10.1007/s41980-020-00496-1

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  • DOI: https://doi.org/10.1007/s41980-020-00496-1

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