TY - JOUR

T1 - Does the ratio of Laplace transforms of powers of a function identify the function?

AU - Konstantopoulos, Takis

AU - Yuan, Linglong

N1 - Publisher Copyright:
© 2020 Elsevier Inc.

PY - 2021/2/1

Y1 - 2021/2/1

N2 - We study the following question: if f is a nonzero measurable function on [0,∞) and m and n are distinct nonnegative integers, does the ratio fnˆ/fmˆ of the Laplace transforms of the powers fn and fm of f uniquely determine f? By the inverse Laplace transform, the answer is yes if m or n is zero. Under some assumptions on the smoothness of f, we show that the answer in the general case is also affirmative. The question arose from a problem in economics, specifically in auction theory, where f is the cumulative distribution function of a certain random variable. This is also discussed.

AB - We study the following question: if f is a nonzero measurable function on [0,∞) and m and n are distinct nonnegative integers, does the ratio fnˆ/fmˆ of the Laplace transforms of the powers fn and fm of f uniquely determine f? By the inverse Laplace transform, the answer is yes if m or n is zero. Under some assumptions on the smoothness of f, we show that the answer in the general case is also affirmative. The question arose from a problem in economics, specifically in auction theory, where f is the cumulative distribution function of a certain random variable. This is also discussed.

KW - Auction theory

KW - Laplace transform

KW - Order statistics

UR - http://www.scopus.com/inward/record.url?scp=85090754221&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2020.124568

DO - 10.1016/j.jmaa.2020.124568

M3 - Article

AN - SCOPUS:85090754221

SN - 0022-247X

VL - 494

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 124568

ER -