A version of Watson lemma for Laplace integrals and some applications
Stanislas KupinUniversité de Bordeaux I, Talence, France
Sergey NabokoSt. Petersburg University, Russian Federation
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Let be a bounded measurable function. Suppose that at logarithmic (or -logarithmic) rate as . We consider the Laplace integral of the function , i.e.,
and obtain its asymptotics for , which is a version of the classical Watson’s lemma for the integral. Actually, the result is proved for a larger class of “slowly oscillating” functions satisfying some mild regularity conditions.