MR3052747 A. BOUMENIR A. BOUMENIR An Inverse Problem for a Parabolic Convolution Equation Funkcialaj Ekvacioj. Serio Internacia 55 2012 447--456 http://fe.math.kobe-u.ac.jp/FE/FullPapers/55-3/55_447.pdf http://www.ams.org/mathscinet-getitem?mr=MR3052747 We consider an inverse problem involving a parabolic equation which contains an integral operator of convolution type. We show that we can approximate its kernel by using three readings of a certain weighted average of the solution. In case the kernel is known to be band limited then the three measurements are enough for its full recovery. Inverse problem, Heat equation, Gelfand-Levitan theory. 35K10, 34K29, 35R30. 55-447 2012 An Inverse Problem for a Parabolic Convolution Equation A. BOUMENIR A. BOUMENIR 1 Avdonin, S. A.; Ivanov, S. A. Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems Cambridge University Press, Cambridge 1995 MR1366650
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