engleski

Error estimates for approximations of the Mellin transform in Lp spaces

In this talk error estimates of the approximations in complex domain for the Mellin transform M(f) are given for real functions f which vanish beyond a finite domain [a, b]⊂<0, ∞> and such that f′∈Lp[a, b]. The estimate of the difference between E(zln a, zln b)(L(a, b))⁻¹∫_{;a};^{;b};f(t)dt and M(f)(z) is given, where E(z, w) is exponential mean of complex numbers z and w, and L(a, b) is logarithmic mean of real numbers a and b. New inequalities concerning the estimate of the difference between two Mellin transforms are presented. These are used to obtain two associated numerical quadrature rules and error bounds for their reminders.

Mellin transform; approximations in complex domain

nije evidentirano