Proceedings of the Japan Academy

Oscillatory integrals of symbols of pseudo-differential operators on $R^n$ and operators of Fredholm type

Article information

Source
Proc. Japan Acad., Volume 49, Number 6 (1973), 397-402.

Dates
First available in Project Euclid: 20 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195519291

Digital Object Identifier
doi:10.3792/pja/1195519291

Mathematical Reviews number (MathSciNet)
MR0355693

Zentralblatt MATH identifier
0272.47032

Subjects
Primary: 47G05
Secondary: 35S05: Pseudodifferential operators

Citation

Kumano-Go, Hitoshi; Taniguchi, Kazuo. Oscillatory integrals of symbols of pseudo-differential operators on $R^n$ and operators of Fredholm type. Proc. Japan Acad. 49 (1973), no. 6, 397--402. doi:10.3792/pja/1195519291. https://projecteuclid.org/euclid.pja/1195519291

References

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• [2] V. V. Grushin: Pseudo-differential operators on Rn with bounded symbols. Functional Anal. Appl., 4, 202-212 (1970).
• [3] V. V. Grushin: Hypoelliptic differential equations and pseudo-differential operators with operator-valued symbols. Mat. Sb., 88(130), 504-521 (1972) (in Russian).
• [4] L. Hormander: Pseudo-differential operators and hypoelliptic equations. Proc. Symposium on Singular Integrals. Amer. Math. Soc, 10, 138-183 (1967).
• [5] Y. Kannai: An unsolvable hypoelliptic differential operator. Israel J. Math., 9, 306-315 (1971).
• [6] H. Kumano-go: Algebras of pseudo-differential operators. J. Fac. Sei. Univ. Tokyo, 17, 31-51 (1970).
• [7] H. Kumano-go: On the index of hypoelliptic pseudo-differential operators on Rn. Proc. Japan Acad., 48, 402-407 (1972).
• [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)).
• [10] S. Mizohata: Solutions nulles et solutions non analytiques. J. Math. Kyoto Univ., 1, 271-302 (1962).