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
In this paper, the concept of para-Fourier integral operators is introduced by studying Fourier integral operators with irregular phase functions, and some basic properties of the para-Fourier integral operators are g...In this paper, the concept of para-Fourier integral operators is introduced by studying Fourier integral operators with irregular phase functions, and some basic properties of the para-Fourier integral operators are given.展开更多
This work studies the canonical representations (Berezin representations) for para-Hermitian symmetric spaces of rank one. These spaces are exhausted up to the covering by spaces?G/H?with G = SL(n,R),H = GL(n-1,R)?. F...This work studies the canonical representations (Berezin representations) for para-Hermitian symmetric spaces of rank one. These spaces are exhausted up to the covering by spaces?G/H?with G = SL(n,R),H = GL(n-1,R)?. For Hermitian symmetric spaces G/K, canonical representations were introduced by Berezin and Vershik-Gelfand-Graev. They are unitary with respect to some invariant non-local inner product (the Berezin form). We consider canonical representations in a wider sense: we give up the condition of unitarity and let these representations act on spaces of distributions. For our spaces G/H, the canonical representations turn out to be tensor products of representations of maximal degenerate series and contragredient representations. We decompose the canonical representations into irreducible constituents and decompose boundary representations.展开更多
In this paper, we prove the Egorov theorem for paradlfferentlal operators based on the theory of para-Fourier integral operators. Obviously, this theorem is imporfant for the study on properlies of paradifferential op...In this paper, we prove the Egorov theorem for paradlfferentlal operators based on the theory of para-Fourier integral operators. Obviously, this theorem is imporfant for the study on properlies of paradifferential operators. Before proving this theorem, we introduce the concept of adjoint para-Fourier integral operators and establish some of its properties.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘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.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, the concept of para-Fourier integral operators is introduced by studying Fourier integral operators with irregular phase functions, and some basic properties of the para-Fourier integral operators are given.
文摘This work studies the canonical representations (Berezin representations) for para-Hermitian symmetric spaces of rank one. These spaces are exhausted up to the covering by spaces?G/H?with G = SL(n,R),H = GL(n-1,R)?. For Hermitian symmetric spaces G/K, canonical representations were introduced by Berezin and Vershik-Gelfand-Graev. They are unitary with respect to some invariant non-local inner product (the Berezin form). We consider canonical representations in a wider sense: we give up the condition of unitarity and let these representations act on spaces of distributions. For our spaces G/H, the canonical representations turn out to be tensor products of representations of maximal degenerate series and contragredient representations. We decompose the canonical representations into irreducible constituents and decompose boundary representations.
基金Project supported by the National Natural Science Foundation of China
文摘In this paper, we prove the Egorov theorem for paradlfferentlal operators based on the theory of para-Fourier integral operators. Obviously, this theorem is imporfant for the study on properlies of paradifferential operators. Before proving this theorem, we introduce the concept of adjoint para-Fourier integral operators and establish some of its properties.
