On the asymptotic behaviour of the Green operators for elliptic boundary problems and the pure imaginary powers of some second order operators

Daisuke FUJIWARA

doi:10.2969/jmsj/02140481

Daisuke FUJIWARA

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JOURNAL FREE ACCESS

1969 Volume 21 Issue 4 Pages 481-522

DOI https://doi.org/10.2969/jmsj/02140481

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Published: 1969 Received: July 08, 1968 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math., 15 (1962), 119-147.
2) S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutionsof elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 17 (1964), 35-92.
3) A. P. Calderón, Lebesgue spaces of differentiable functions and distributions, Proc. Symp. Pure Math. 4, “Partial differential equations” (1961), 33-92.
4) A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), 113-190.
5) A. P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math., 79 (1957), 901-921.
6) D. Fujiwara, On a special class of pseudo-differential operators, J. Fac. Sci. Univ. Tokyo Sect. I, 14 (1967), 221-249.
7) D. Fujiwara, On an asymptotic formula of trace of elliptic operators operating on a vector bundles on a compact manifold, Proc. Japan Acad., 43 (1967), 426-428.
8) D. Fujiwara, On the asymptotic formula for the Green operator of elliptic operators on compact manifolds, J. Fac. Sci. Univ. Tokyo Sect. I, 14 (1967), 251-283.
9) D. Fujiwara, L^p-theory for characterizing the domain of the fractional powers of -Δ in the half space, J. Fac. Sci. Univ. Tokyo Sect. I, 15 (1968), to appear.
10) A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Memoire of the A.M.S. 1955.
11) P. Grisvard, Caractérisation de quelques espaces d'interpolation, Arch. Rational Mech. Anal., 25 (1967), 40-63.
12) L. Hörmander, Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math., 83 (1966), 129-209.
13) J. L. Lions, Remarques sur les espaces d'interpolation et les problèmes aux limites, Coll. C. N. R. S. sur “Les équation aux dérivées partielles”, Paris, (1962), 75-86.
14) S. G. Mikhilin, Multi-dimensional singular integrals and integral equations, Pergamon press (1965).
15) L. B. Monvel, Pseudo-noyaux de Poisson et opérateur pseudo-différèntiels sur une variété à bord, C. R. Acad. Sci. Paris, 261 (1965), 3927-3930.
16) L. Schwartz, Théorie des distributions, III^e ed. Hermann, Paris, (1966).
17) R. T. Seeley, Complex powers of an elliptic operator, Proc. of Symp. in Pure Math. on Singular integrals (1967), 288-387.
18) R. T. Seeley, The resolvent of an elliptic boundary problem, Estratto da atti del congresso su le equazioni alle derivate parziali, Bologna, (1967), 164-168.
19) H. Whitney, Analytic extension of differentiable functions defined in closed sets, Trans. Amer. Math. Soc., 36 (1934), 63-89.
20) K. Yosida, Functional analysis, Springer (1965).

Right : [1] S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math., 15 (1962), 119-147.
[2] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 17 (1964), 35-92.
[3] A. P. Calderón, Lebesgue spaces of differentiable functions and distributions, Proc. Symp. Pure Math. 4, “Partial differential equations” (1961), 33-92.
[4] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), 113-190.
[5] A. P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math., 79 (1957), 901-921.
[6] D. Fujiwara, On a special class of pseudo-differential operators, J. Fac. Sci. Univ. Tokyo Sect. I, 14 (1967), 221-249.
[7] D. Fujiwara, On an asymptotic formula of trace of elliptic operators operating on a vector bundles on a compact manifold, Proc. Japan Acad., 43 (1967), 426-428.
[8] D. Fujiwara, On the asymptotic formula for the Green operator of elliptic operators on compact manifolds, J. Fac. Sci. Univ. Tokyo Sect. I, 14 (1967), 251-283.
[9] D. Fujiwara, L^p-theory for characterizing the domain of the fractional powers of -Δ in the half space, J. Fac. Sci. Univ. Tokyo Sect. I, 15 (1968), to appear.
[10] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Memoire of the A. M. S. 1955.
[11] P. Grisvard, Caractérisation de quelques espaces d'interpolation, Arch. Rational Mech. Anal., 25 (1967), 40-63.
[12] L. Hörmander, Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math., 83 (1966), 129-209.
[13] J. L. Lions, Remarques sur les espaces d'interpolation et les problèmes aux limites, Coll. C. N. R. S. sur “Les équation aux dérivées partielles”, Paris, (1962), 75-86.
[14] S. G. Mikhilin, Multi-dimensional singular integrals and integral equations, Pergamon press (1965).
[15] L. B. Monvel, Pseudo-noyaux de Poisson et opérateur pseudo-différèntiels sur une variété à bord, C. R. Acad. Sci. Paris, 261 (1965), 3927-3930.
[16] L. Schwartz, Théorie des distributions, III^e ed. Hermann, Paris, (1966).
[17] R. T. Seeley, Complex powers of an elliptic operator, Proc. of Symp. in Pure Math. on Singular integrals (1967), 288-387.
[18] R. T. Seeley, The resolvent of an elliptic boundary problem, Estratto da atti del congresso su le equazioni alle derivate parziali, Bologna, (1967), 164-168.
[19] H. Whitney, Analytic extension of differentiable functions defined in closed sets, Trans. Amer. Math. Soc., 36 (1934), 63-89.
[20] K. Yosida, Functional analysis, Springer (1965).

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