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Dedicated to Professor Yoichiro Takahashi on the occasion of his 60th birthday Abstract. N. Ikeda and the author established a mapping from a class of Gaussian measures parameterized by linear combina...tions of Dirac measures on $ R $ to that of reflectionless potentials. The bijectivity of the mapping was shown by the author, and was extended to a class of more general Gaussian measures. In this paper, a brief review on the bijection and its application to the KdV equation is given first. Next another application to the stochastic KdV equation is discussed. Finally presented is an alternative approach to the bijection via the linear filtering theory.続きを見る
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