Error Estimates of Approximations for the Complex Valued Integral Transforms

Andrea Aglić Aljinović ()
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Andrea Aglić Aljinović: University of Zagreb, Faculty of Electrical Engineering and Computing

A chapter in Differential and Integral Inequalities, 2019, pp 21-47 from Springer

Abstract: Abstract In this survey paper error estimates of approximations in complex domain for the Laplace and Mellin transform are given for functions f which vanish beyond a finite domain a , b ⊂ 0 , ∞ $$\left [ a,b\right ] \subset \left [ 0,\infty \right \rangle $$ and whose derivative belongs to L p a , b $$L_{p}\left [ a,b \right ] $$ . New inequalities involving integral transform of f, integral mean of f and exponential and logarithmic mean of the endpoints of the domain of f are presented. These estimates enable us to obtain two associated numerical quadrature rules for each transform and error bounds of their remainders.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-27407-8_2

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DOI: 10.1007/978-3-030-27407-8_2

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