The fundamental solution for a parabolic pseudo-differential operator and parametrices for degenerate operators

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The fundamental solution for a parabolic pseudo-differential operator and parametrices for degenerate operators

Chisato Tsutsumi

Source: Proc. Japan Acad. Volume 51, Number 2 (1975), 103-108.

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Primary Subjects: 35S05

Secondary Subjects: 47G05

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Permanent link to this document: http://projecteuclid.org/euclid.pja/1195518695
Mathematical Reviews number (MathSciNet): MR0380172
Zentralblatt MATH identifier: 0321.35068
Digital Object Identifier: doi:10.3792/pja/1195518695

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References

[1] Beals, R.: A general calculus of pseudodifferential operators (to appear).

Mathematical Reviews (MathSciNet): MR367730

Zentralblatt MATH: 0343.35078

Digital Object Identifier: doi:10.1215/S0012-7094-75-04201-5

Project Euclid: euclid.dmj/1077310893

[2] Grushin, V. V.: Hypoelliptic differential equations and pseudo-differential operators with operator-valued symbols. Mat. Sb., 88, 504-521 (1972).

Mathematical Reviews (MathSciNet): MR316879

Zentralblatt MATH: 0243.35020

[3] Hormander, L.: Hypoelliptic second order differential equations. Acta Math., 119, 147-174 (1967).

Mathematical Reviews (MathSciNet): MR222474

Zentralblatt MATH: 0156.10701

Digital Object Identifier: doi:10.1007/BF02392081

[4] Hoel, C.: Fundamental solutions of some degenerate operators. J. Differential Equations, 15, 379-417 (1974).

Mathematical Reviews (MathSciNet): MR346306

Zentralblatt MATH: 0286.35039

Digital Object Identifier: doi:10.1016/0022-0396(74)90065-5

[5] Kumano-go, H.: Pseudo-differential operators of multiple symbol and the Calderon-Vaillancourt theorem. J. Math. Soc. Japan, 27, 113-120 (1975).

Mathematical Reviews (MathSciNet): MR361937

Zentralblatt MATH: 0294.35068

Digital Object Identifier: doi:10.2969/jmsj/02710113

Project Euclid: euclid.jmsj/1240434886

[6] Kumano-go, H., and Taniguchi, K.: Oscillatory integrals of symbols of operators on Rn and operators of Freadholm type. Proc. Japan Acad., 49, 397-402 (1973).

Mathematical Reviews (MathSciNet): MR355693

Zentralblatt MATH: 0272.47032

Digital Object Identifier: doi:10.3792/pja/1195519291

Project Euclid: euclid.pja/1195519291

[7] Kumano-go, H., and Tsutsumi, C.: Complex powers of hypoelliptic pseudo-differential operators with applications. Osaka J. Math., 10, 147-174 (1973).

Mathematical Reviews (MathSciNet): MR328392

Zentralblatt MATH: 0264.35019

Project Euclid: euclid.ojm/1200694131

[8] Mizohata, S.: Solutions nulles et solutions non analytiques. J. Math. Kyoto Univ., 1, 271-302 (1962).

Mathematical Reviews (MathSciNet): MR142873

Zentralblatt MATH: 0106.29601

Project Euclid: euclid.kjm/1250525061

[9] Sjostrand, J.: Parametrices for pseudodifferential operators with multiple-characteristics. Ark. Mat., 12, 85-130 (1974).

Mathematical Reviews (MathSciNet): MR352749

Zentralblatt MATH: 0317.35076

Digital Object Identifier: doi:10.1007/BF02384749

[10] Tsutsumi, C.: The fundamental solution for a degenerate parabolic pseudo-differential operator. Proc. Japan Acad., 50, 11-15 (1974).