2022-01-22T03:08:29Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000120322021-03-01T11:36:31ZRegularization of differential equations on a Hilhert space and non-associative algebra.Hilbert空間の微分方程式の正則化と非結合代数TANABE, Nobuhiko36885Laplace operator on a Hilbert space can not even act on the metric function. To overcome this difficult, we defined regularization of Laplacian. In particular, we computed polar coordinate expression of regularized Laplacian which can not do without regularization[2]. We try to rewrite given regularized spherical Laplacian from the point of quantum mechanics on an infinite dimensional space. We eliminate the difficulty comes from infinite dimensional property of the space, by introducing a Jordan algebra, which is non-associative. In finite dimensional case, Jordan algebra has been used to define Dirac kind operator ([5],[10]). We adopt this argument to the infinite dimensional case and define an infinite dimensional Dirac kind operator.Article信州大学理学部紀要 34(2): 111-126(2000)departmental bulletin paper信州大学理学部2000-03-30application/pdf信州大学理学部紀要2341111260583-063XAA00697923https://soar-ir.repo.nii.ac.jp/record/12032/files/Science34-02-03.pdfjpn