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Oscillatory integrals of symbols of pseudo-differential operators on R\(^n\) and operators of Fredholm type. (English) Zbl 0272.47032


MSC:

47Gxx Integral, integro-differential, and pseudodifferential operators
35S05 Pseudodifferential operators as generalizations of partial differential operators
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[1] A. P. Calderon and R. Vaillancourt: A class of bounded pseudo-differential operators. Proc. Nat. Acad. Sci. USA, 69, 1185-1187 (1972). JSTOR: · Zbl 0244.35074
[2] V. V. Grushin: Pseudo-differential operators on Rn with bounded symbols. Functional Anal. Appl., 4, 202-212 (1970). · Zbl 0223.35084
[3] V. V. Grushin: Hypoelliptic differential equations and pseudo-differential operators with operator-valued symbols. Mat. Sb., 88(130), 504-521 (1972) (in Russian). · Zbl 0243.35020
[4] L. Hormander: Pseudo-differential operators and hypoelliptic equations. Proc. Symposium on Singular Integrals. Amer. Math. Soc, 10, 138-183 (1967). · Zbl 0167.09603
[5] Y. Kannai: An unsolvable hypoelliptic differential operator. Israel J. Math., 9, 306-315 (1971). · Zbl 0211.40601
[6] H. Kumano-go: Algebras of pseudo-differential operators. J. Fac. Sei. Univ. Tokyo, 17, 31-51 (1970). · Zbl 0206.10501
[7] H. Kumano-go: On the index of hypoelliptic pseudo-differential operators on Rn. Proc. Japan Acad., 48, 402-407 (1972). · Zbl 0252.35066
[8] H. Kumano-go: Oscillatory integrals of symbols of pseudo-differential operators and the local solvability theorem of Nirenberg and Treves. Katata Simposium on Partial Differential Equation, pp. 166-191 (1972).
[9] H. Kumano-go and C. Tsutsumi: Complex powers of hypoelliptic pseudo-differential operators with applications (to appear in Osaka J. Math., 10 (1973)). · Zbl 0264.35019
[10] S. Mizohata: Solutions nulles et solutions non analytiques. J. Math. Kyoto Univ., 1, 271-302 (1962). · Zbl 0106.29601
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