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Micro-local analysis of prehomogeneous vector spaces. (English) Zbl 0456.58034

MSC:
58J99 Partial differential equations on manifolds; differential operators
58J15 Relations of PDEs on manifolds with hyperfunctions
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
20G05 Representation theory for linear algebraic groups
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[1] Sato, M., Kimura, T.: A classification of irreducible prehomogeneous vector spaces and their relative invariants. Nagoya Math. J,65, 1-155 (1977) · Zbl 0321.14030
[2] Sato, M., Kawai, T., Kashiwara, M.: Hyperfunctions and Pseudo-differential Equations. Lecture Notes in Mathematics 287, Berlin Heidelberg New York: Springer-Verlag · Zbl 0277.46039
[3] Sato, M., Shintani, T.: On zeta-functions associated with prehomogeneous vector spaces. Ann. of Math.,100, 131-170 (1974) · Zbl 0309.10014 · doi:10.2307/1970844
[4] Sato, M.: Theory of prehomogeneous vector spaces, (noted by T. Shintani in Japanese). Sugaku no ayumi,15, 85-157 (1970)
[5] Shintani, T.: On Dirichlet series whose coefficients are class-numbers of integral binary cubic forms. J. Math. Soc. Japan,24, 132-188 (1972) · Zbl 0227.10031 · doi:10.2969/jmsj/02410132
[6] Servedio, F.: Affine Open Orbits, Reductive Isotropy Groups, and Dominant Gradient Morphisms: A Theorem of Mikio Sato. Pacific J. of Math.,72, 537-545 (1977) · Zbl 0346.14019
[7] Kashiwara, M.: B-Functions and Holonomic Systems (Rationality ofb-functions). Inv.38, 33-53 (1976) · Zbl 0354.35082 · doi:10.1007/BF01390168
[8] Kashiwara, M., Kawai, T.: On holonomic systems for \(\mathop \Pi \limits_{l = 1}^N (f_1 + \sqrt { - 1} 0)^{\lambda t} \) , RIMS, to appear · Zbl 0449.35067
[9] Kashiwara, M., Kawai, T.: Holonomic systems of micro-differential equations III, to appear · Zbl 0361.35064
[10] Sato, M., Kashiwara, M.: The determinant of matrices of pseudo-differential operators. Proc. Japan Acad.51, 17-19 (1975) · Zbl 0337.35067 · doi:10.3792/pja/1195518723
[11] Carath√©odory, C.: Calculus of Variations and Partial Differential Equations of the First Order, Part 1, Amsterdam: Holden-Day 1965, Translated from the German original, 1935 · Zbl 0014.06803
[12] Oshima, T.: Singularities in contact geometry and degenerate pseudo-differential equations. J. Fac. Sci. Univ. Tokyo Sec. IA21, 43-83 (1974) · Zbl 0282.35070
[13] Kashiwara, M., Oshima, T.: Systems of differential equations with regular singularities and their boundary value problems. Ann. of Math.,106, 145-200 (1977) · Zbl 0358.35073 · doi:10.2307/1971163
[14] Bernstein, I.N.: The analytic continuation of generalized functions with respect to a parameter. Functional Anal. Appl.6, 26-40 (1972)
[15] Kimura, T.: Theb-functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces, to appear
[16] Bijork, J.E.: Rings of differential operators, Amsterdam: North-Holland 1979
[17] Boutet de Monvel-Kree: Pseudo-differential operators and Gevrey classes. Ann. Inst. Fourier17, 295-323 (1967) · Zbl 0195.14403
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