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

被引：0
|
作者：
Maan, Jeetendrasingh [1 ]
Negrin, E. R. [2 ]
机构：
[1] Natl Inst Technol, Dept Math & Sci Comp, Hamirpur 177005, India
[2] Univ La Laguna ULL, Dept Anal Matemat, 38271 San Cristobal la Laguna, Tenerife, Spain
来源：
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES | 2024年
关键词：
Generalized Stieltjes-Poisson transform; Inversion formula; Parseval-type relations; Weighted Lebesgue spaces; Exchange formulae; Distributions of compact support; Asymptotic behaviours;
D O I：
10.1007/s40863-024-00462-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：22
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    [J]. Rendiconti del Circolo Matematico di Palermo Series 2, 2023, 72 : 3551 - 3561
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