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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The dual Weierstrass-Laguerre transform


Author: Deborah Tepper Haimo
Journal: Trans. Amer. Math. Soc. 290 (1985), 597-613
MSC: Primary 44A15; Secondary 35C15
MathSciNet review: 792814
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Abstract: An inversion algorithm is derived for the dual Weierstrass-Laguerre transform $ \int_0^\infty {{g_\alpha }(x,y;1)\varphi (y){y^\alpha }{e^{ - y}}/(\alpha + 1)dy} $, where the function $ {g_\alpha }(x,y,t)$ is associated with the source solution of the Laguerre differential heat equation $ x{u_{xx}}(x,t) = (\alpha + 1 - x){u_x}(x,t) = {u_t}(x,t)$. Correspondingly, sufficient conditions are established for a function to be represented by a Weierstrass-Laguerre Stieltjes transform $ \int_0^\infty {{g_\alpha }(x,y;1)\;d\beta (y)} $ of a nondecreasing function $ \beta $.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0792814-X
PII: S 0002-9947(1985)0792814-X
Article copyright: © Copyright 1985 American Mathematical Society