Bulletin of the American Mathematical Society

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Book Information:

Author: H. O. Cordes
Title: Spectral theory of linear differential operators and comparison algebras
Additional book information: London Mathematical Society Lecture Notes Series, vol. 76, Cambridge University Press, Cambridge, New York, Melbourne, 1987, ix + 342 pp., $29.95. ISBN 0-521-28443-0.

André Unterberger and Juliane Bokobza, Les opérateurs de Calderon-Zygmund précisés, C. R. Acad. Sci. Paris 259 (1964), 1612–1614 (French). MR 176360

A.-P. Calderón, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80 (1958), 16–36. MR 104925, DOI 10.2307/2372819

H. O. Cordes, An algebra of singular integral operators with two symbol homomorphisms, Bull. Amer. Math. Soc. 75 (1969), 37–42. MR 234320, DOI 10.1090/S0002-9904-1969-12137-3

Jeff Cheeger, Mikhail Gromov, and Michael Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geometry 17 (1982), no. 1, 15–53. MR 658471

A.-P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901–921. MR 100768, DOI 10.2307/2372441

A. S. Dynin, Singular operators of arbitrary order on a manifold, Dokl. Akad. Nauk SSSR 141 (1961), 21–23 (Russian). MR 0155205

Alexander Dynin, Inversion problem for singular integral operators: $C^{\ast }$-approach, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), no. 10, 4668–4670. MR 507929, DOI 10.1073/pnas.75.10.4668

Alexander Dynin, Algebras generated by classical pseudodifferential operators on open Riemannian manifolds, Operator theory: operator algebras and applications, Part 2 (Durham, NH, 1988) Proc. Sympos. Pure Math., vol. 51, Amer. Math. Soc., Providence, RI, 1990, pp. 93–98. MR 1077423

[E] J. Eichorn, Elliptic differential operators on non-compact manifolds, Seminar Analysis of the Karl-Weierstrass-Institute 1986/1987, Teubner-Texte zur Mathematik vol. 106, pp. 4-170, Teubner, Leipzig, 1988.

Lars Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501–517. MR 180740, DOI 10.1002/cpa.3160180307

I. C. Gohberg, On the theory of multidimensional singular integral equations, Soviet Math. Dokl. 1 (1960), 960–963. MR 0124704

J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269–305. MR 176362, DOI 10.1002/cpa.3160180121

[M] R. Melrose, Pseudodifferential operators with corners, Manuscript MIT, Boston, 1987.

B. A. Plamenevskiĭ, Algebry psevdodifferentsial′nykh operatorov, “Nauka”, Moscow, 1986 (Russian). MR 869253

[R] R. Roe, Elliptic operators, topology and asymptotic methods, Cambridge Univ. Press, 1988.

[S] B. W. Schultze, Pseudodifferential operators on manifolds with singularities, Akad. Verlagsges, Leipzig, North-Holland (in preparation).

[BU] J. Bokobza and A. Unterberger, Opérateurs de Calderón-Zygmund précisés, C. R. Acad. Sci. Paris 259 (1964), 1612-1614. MR 0176360




[C1] A. Calderón, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80 (1958), 16-36. MR 104925




[C2] H. Cordes, An algebra of singular integral operators with two symbol homomorphisms, Bull. Amer. Math. Soc. 75 (1969), 37-42. MR 234320




[CGT] J. Cheeger, M. Gromov and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operators, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982), 15-54. MR 658471




[CZ] A. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901-921. MR 100768




[D1] A. Dynin, Singular integral operators of an arbitrary order on a manifold, Dokl. Akad. Nauk 141 (1961), 21-23 (= Soviet Math. Dokl. 2 (1961), 1375-1377). MR 155205




[D2] A. Dynin, Inversion problem for singular integral operators: C*-approach, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), 4668-4670. MR 507929




[D3] A. Dynin, Algebra generated by classical pseudodifferential operators on open Riemannian manifolds, Preprint (1988). MR 1077423




[E] J. Eichorn, Elliptic differential operators on non-compact manifolds, Seminar Analysis of the Karl-Weierstrass-Institute 1986/1987, Teubner-Texte zur Mathematik vol. 106, pp. 4-170, Teubner, Leipzig, 1988.




[H] L. Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501-517. MR 180740




[G] I. Gohberg, On the theory of multidimensional singular integral operators, Dokl. Akad. Nauk 133 (1960) (= Soviet Math. Dokl. 1 (1960), 960-963). MR 124704




[KN] J. Kohn and L. Nirenberg, An algebra of pseudodifferential operators, Comm. Pure Appl. Math. 18 (1965), 269-305. MR 176362




[M] R. Melrose, Pseudodifferential operators with corners, Manuscript MIT, Boston, 1987.




[P] B. A. Plamenevskij, Algebras of pseudodifferential operators, "Nauka", Moscow, (1986) (Russian). MR 869253




[R] R. Roe, Elliptic operators, topology and asymptotic methods, Cambridge Univ. Press, 1988.




[S] B. W. Schultze, Pseudodifferential operators on manifolds with singularities, Akad. Verlagsges, Leipzig, North-Holland (in preparation).