Let H. be the n-direct proded of Heisenbery group H, P the affine group of Hn. Then P ho a natural unitary representation U on L2(Hn). In this paper,the direct sum decomposition of irreducible invariant closed subspac...Let H. be the n-direct proded of Heisenbery group H, P the affine group of Hn. Then P ho a natural unitary representation U on L2(Hn). In this paper,the direct sum decomposition of irreducible invariant closed subspaces under unitary representation U for L2(Hn) is given. The restrictins of U on these subspaces are square-integrable. The charactedsation of admissible condition is obtained in ierms of the Fourier transform. By seleting appropriately an orthogonal wavelet basis and the wavelet transform,the authors obtain the orthogonal direct chin decomposinon of function space L2(P,dμl).展开更多
Abstract In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another conside...Abstract In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another consideration concerns the entropy production across the shocks. The latter is natural from the physical point of view, but is not sufficient in its straightforward formulation, if the system is not genuinely nonlinear. In this paper we propose the principles of increasing entropy production and that of the superposition of shocks. These principles are shown to be equivalent to the admissibility criterion.展开更多
文摘Let H. be the n-direct proded of Heisenbery group H, P the affine group of Hn. Then P ho a natural unitary representation U on L2(Hn). In this paper,the direct sum decomposition of irreducible invariant closed subspaces under unitary representation U for L2(Hn) is given. The restrictins of U on these subspaces are square-integrable. The charactedsation of admissible condition is obtained in ierms of the Fourier transform. By seleting appropriately an orthogonal wavelet basis and the wavelet transform,the authors obtain the orthogonal direct chin decomposinon of function space L2(P,dμl).
基金Partially supported by the NSF (Grant DMS-9803323)Supported by fondi MIUR Progetto di interesse Nazionale Problemi Matematici Non Lineari di Propagazionee Stabilitd nei Modelli del Continuo Coordinatore T.Ruggeri,by the GNFM-INDAM,and by the Istitut
文摘Abstract In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another consideration concerns the entropy production across the shocks. The latter is natural from the physical point of view, but is not sufficient in its straightforward formulation, if the system is not genuinely nonlinear. In this paper we propose the principles of increasing entropy production and that of the superposition of shocks. These principles are shown to be equivalent to the admissibility criterion.
