We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences....We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.展开更多
Let（S）L<sup>2</sup>（S’（IR）,μ）（S）<sup>*</sup> be the Gel’fand triple over the white noise space （S’（IR）,μ）.Let（e<sub>n</sub>,n≥0）be the ONB of L<sup>2</s...Let（S）L<sup>2</sup>（S’（IR）,μ）（S）<sup>*</sup> be the Gel’fand triple over the white noise space （S’（IR）,μ）.Let（e<sub>n</sub>,n≥0）be the ONB of L<sup>2</sup>（IR）consisting of the eigenfunctions of the s.a. operator-（d/（dt））<sup>2</sup>+1+t<sup>2</sup>.In this paper the Euler operator △<sub>E</sub> is defined as the sum ∑<sub>i</sub>【,e<sub>i</sub>)<sub>i</sub>, where <sub>i</sub> stands for the differential operator D<sub>ei</sub>.It is shown that △<sub>E</sub> is the infinitesimal gen- erator of the semigroup（T<sub>t</sub>）,where(T<sub>t</sub>)（x）=（e<sup>t</sup>x）for ∈（S）.Similarly to the finite dimensional case,the λ-order homogeneous test functionals are characterized by the Euler equa- tion:△<sub>E</sub>=λ.Via this characterization the λ-order homogeneous Hida distributions are defined and their properties are worked out.展开更多
文摘We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.
基金Supported by the National Natural Science Foundation of China
文摘Let（S）L<sup>2</sup>（S’（IR）,μ）（S）<sup>*</sup> be the Gel’fand triple over the white noise space （S’（IR）,μ）.Let（e<sub>n</sub>,n≥0）be the ONB of L<sup>2</sup>（IR）consisting of the eigenfunctions of the s.a. operator-（d/（dt））<sup>2</sup>+1+t<sup>2</sup>.In this paper the Euler operator △<sub>E</sub> is defined as the sum ∑<sub>i</sub>【,e<sub>i</sub>)<sub>i</sub>, where <sub>i</sub> stands for the differential operator D<sub>ei</sub>.It is shown that △<sub>E</sub> is the infinitesimal gen- erator of the semigroup（T<sub>t</sub>）,where(T<sub>t</sub>)（x）=（e<sup>t</sup>x）for ∈（S）.Similarly to the finite dimensional case,the λ-order homogeneous test functionals are characterized by the Euler equa- tion:△<sub>E</sub>=λ.Via this characterization the λ-order homogeneous Hida distributions are defined and their properties are worked out.
