The generalized Stieltjes–Poisson transform over Lebesgue spaces and distributions of compact support

The generalized Stieltjes–Poisson transform over Lebesgue spaces and distributions of compact support

This paper investigates the generalized Stieltjes–Poisson transform, deriving a real inversion formula and exploring its asymptotic behaviours over Lebesgue spaces. It further establishes a Parseval-type relations for this transform over Lebesgue spaces. We also obtain exchange formulae for the gene...

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Veröffentlicht in:São Paulo Journal of Mathematical Sciences 2024-08, Vol.18 (2), p.1839-1860
Hauptverfasser: Maan, Jeetendrasingh, Negrín, E. R.
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Asymptotic properties
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description This paper investigates the generalized Stieltjes–Poisson transform, deriving a real inversion formula and exploring its asymptotic behaviours over Lebesgue spaces. It further establishes a Parseval-type relations for this transform over Lebesgue spaces. We also obtain exchange formulae for the generalized Stieltjes–Poisson transform via Mellin-type convolutions over weighted Lebesgue spaces. Additionally, the study extends the transform to derive an inversion formula and analyze asymptotic behaviours over distributions of compact support.
doi_str_mv 10.1007/s40863-024-00462-3
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2306-9028
language eng
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subjects Asymptotic properties
Mathematics
Mathematics and Statistics
Original Article
title The generalized Stieltjes–Poisson transform over Lebesgue spaces and distributions of compact support
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