arXiv 2211.034352022-11-07math.CA

Upper bounds and asymptotic expansion for Macdonald's function and the summability of the Kontorovich-Lebedev integrals

S. Yakubovich

英文摘要：

Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function $K_{iτ}(x)$. The results can be applied, for instance, to study the summability of the divergent Kontorovich-Lebedev integrals in the sense of Jones. Namely, we answer affirmatively a question (cf. [6]) whether these integrals converge for even entire functions of the exponential type in a weak sense.

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