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gr(D_n) and gr(ε_p) Are Not Noetherian Rings With Pure Dimension
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作者 吴泉水 《Chinese Science Bulletin》 SCIE EI CAS 1993年第13期1060-1062,共3页
A commutative Noetherian ring R is called a regular Noetherian ring with pure dimension n, if for any maximal ideal m of R, gl.dimR_m=n, where R_m is the localization of R at the maximal ideal m. It is well known that... A commutative Noetherian ring R is called a regular Noetherian ring with pure dimension n, if for any maximal ideal m of R, gl.dimR_m=n, where R_m is the localization of R at the maximal ideal m. It is well known that if R is a finitely generated commutative algebra over some field, R is integral and gl. dimR【∞, then R is a regular Noetherian ring with pure dimension. Let D(V) be the ring of differential operators over the non-singular n-dimensional irreducible algebraic variety V. Then gr(D(V)) is a 展开更多
关键词 RINGS of DIFFERENTIAL OPERATORS RINGS of the germs of microlocal DIFFERENTIAL OPERATORS PURE dimension.
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Energy densities of semilinear wave equations with oscillatory initial data
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作者 尹会成 《Science China Mathematics》 SCIE 1997年第10期1052-1064,共13页
Microlocal defect measures have been used to study the energy densities of scmilinear wave equations with oscillatory initial data.An "open problem" in literature is solved.
关键词 nonlinear GEOMETRIC optics ENERGY density microlocal defect MEASURE RADON measure.
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Semi-classical analysis on H-type groups Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday
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作者 Clotilde Fermanian Kammerer Véronique Fischer 《Science China Mathematics》 SCIE CSCD 2019年第6期1057-1086,共30页
In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic ca... In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we define the semi-classical measures of bounded families of square integrable functions which consist of a pair formed by a measure defined on the product of the group and its unitary dual, and by a field of trace class positive operators acting on the Hilbert spaces of the representations. We illustrate the theory by analyzing examples, which show in particular that this semi-classical analysis takes into account the finite-dimensional representations of the group, even though they are negligible with respect to the Plancherel measure. 展开更多
关键词 H-type groups semi-classical pseudodifferential operators semi-classical measures WIGNER transform asymptotic ANALYSIS microlocal ANALYSIS
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APPLICATION OF PARA-FOURIER INTEGRAL OPERATORS TO PROPAGATION OF NONLINEAR SINGULARITIES
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作者 仇庆久 《Science China Mathematics》 SCIE 1990年第9期1060-1071,共12页
In this paper, the author applies the Egorov Theorem for paradifferential operators established by the theory of para-Fourier integral operators to reduce microlocally paradifferential operators with the principal typ... In this paper, the author applies the Egorov Theorem for paradifferential operators established by the theory of para-Fourier integral operators to reduce microlocally paradifferential operators with the principal type. This reduction is used to study the propagation of singularities for solutions to nonlinear differential equations in the lower frequency range. 展开更多
关键词 (principal type) paradifferential OPERATORS (adjoint) para-Fourier integral OPERATORS microlocal reduction PROPAGATION of SINGULARITIES with lower frequency.
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Decay Rate of Solutions to Hyperbolic System of First Order
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作者 Shuxing Chen Yi Zhou Institute of Mathematics,Fudan University,Shanghai 200433,P.R.China E-mail:sxchen@fudan.ac.cn Fax:021-65646073 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1999年第4期471-484,共14页
In this paper we generalize the global Sobolev inequality introduced by Klainerman in studying wave equation to the hyperbolic system case.We obtain several decay estimates of solutions of a hyperbolic system of first... In this paper we generalize the global Sobolev inequality introduced by Klainerman in studying wave equation to the hyperbolic system case.We obtain several decay estimates of solutions of a hyperbolic system of first order by different norms of initial data.In particular,the result mentioned in Theorem 1.5 offers an optimal decay rate of solutions,if the initial data belongs to the assigned weighted Sobolev space.In the proof of the theorem we reduce the estimate of solutions of a hyperbolic system to the corresponding case for a scalar pseudodifferential equation of the first order,and then establish the required estimate by using microlocal analysis. 展开更多
关键词 Hyperbolic system Decay rate Asymptotic behaviour Microlocal analysis
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A Characterization for the Gevrey-Sobolev Wave Front Set
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作者 Hua CHEN Institute of Mathematics, Wuhan University, Wuhan 430072, P. R. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2001年第2期295-300,共6页
In this note, we use the so-called microlocal energy method to give a characterization of the Gevrey-Sobolev wave front set WF<sub>(</sub>H<sub>T,σ</sub><sup>S</sup> (u), which w... In this note, we use the so-called microlocal energy method to give a characterization of the Gevrey-Sobolev wave front set WF<sub>(</sub>H<sub>T,σ</sub><sup>S</sup> (u), which will be useful in the study of non-linear microlocal analysis in Gevrey classes. 展开更多
关键词 Gevrey-Sobolev space Wave front set Microlocal energy method
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