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- W2108349681 abstract "Duff [3] studied the location and structures of singularities of reflected Riemann functions for hyperbolic mixed problems with constant coefficients in a quarter-space making use of the stationary phase method. However, it seems that it is difficult to apply the method to the study of Riemann functions of more general hyperbolic mixed problems. Matsumura [6] gave an inner estimate of the location of singularities of reflected Riemann functions which correspond to reflected waves, making use of the localization method developed by Atiyah, Bott and Garding [2] and Hormander [4]. In [9] the author proved a localization theorem describing the location of singularities of reflected Riemann functions which correspond to reflected waves, lateral waves and boundary waves. Tsuji [8] also studied the same problem in the cases where operators are homogeneous and obtained similar results. On the other hand outer estimates of singular supports of fundamental solutions for the Cauchy problems were also given in [2]. In this paper we shall be concerned with outer estimates of singular supports of reflected Riemann functions for hyperbolic mixed problems. Now let us state our problems and assumptions. Let R denote the n-dimensional Euclidean space and E its real dual space and write x' = (xl9..., x,,-!), = 0c2,..., *») for the coordinate x = (xl5...9 xn) in R* and £' = (£i,-..,£M-i), t = (£2,'.',&, ! = (& f»+i) for the dual coordinate" @default.
- W2108349681 created "2016-06-24" @default.
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- W2108349681 date "1975-01-01" @default.
- W2108349681 modified "2023-10-16" @default.
- W2108349681 title "Analytic wave front sets of the Riemann functions of hyperbolic mixed problems in a quarter-space" @default.
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- W2108349681 doi "https://doi.org/10.2977/prims/1195191147" @default.
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