This is a preview of subscription content, log in via an institution to check access.
References
[Ag1] S. Agmon,On positivity and decay of solutions of second order elliptic equations on Riemannian manifolds, Proceedings of the International Meeting Dedicated to the Memory of Prof. Carlo Miranda, Naples, Sept. 13–16, 1982, Istituto di Mat. Univ. Napoli.
[Ch1] P. Chernoff,Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Anal.12 (1973), 401–414.
[C1] H. O. Cordes,Elliptic pseudo-differential operators, an abstract theory, Lecture Notes in Math.756. Springer-Verlag, Berlin-Heidelberg-New York, 1979.
[C2] H. O. Cordes,Spectral theory of linear differential operators and comparison algebras, London Math. Soc. Lecture Notes, Vol. 76, Cambridge Univ. Press, 1987.
[CS] H. O. Cordes,Banach algebras, singular integral operators and partial differential equations, Lecture Notes, Lund, 1971 (availble from, the author).
[CWS] H. O. Cordes,Self-adjointness of powers of elliptic operators on non-compact manifolds, Math. Ann.195 (1972), 257–272.
[CEd] H. O. Cordes,Eigenwertdichte von Sturm-Liouville Problemen, Math. Nachr.19 (1958), 64–71.
[CH] H. O. Cordes and E. A. Herman,Gelfand theory of pseudo-differential operators, Am. J. Math.90 (1968), 681–717.
[CTg] H. O. Cordes and T. M. Tang,On the C * -comparison algebra of a class of singular Sturm-Liouville expressions on the real line, Koethe Memorial Volume of Note di Matematica, Univ. di Lecce, to appear.
[Go1] I. Gohberg,On the theory of multi-dimensional singular integral operators, Soviet Math.1 (1960), 960–963.
[IK] T. Ikebe and T. Kato,Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. Rat. Mech. Anal.9 (1962), 77–92.
[Km] E. Kamke,Differentialgleichungen, Loesungsmethoden und Loesungen, Chelsea Publ. Co., New York, 1963.
[Ka1] T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1966.
[MOS] W. Magnus, F. Oberhettinger and R. P. Soni,Formulas and Theorems, for the Special Functions of Mathematical Physics, Springer-Verlag, New York, 1966.
[Re1] F. Rellich,Halbbeschrasenkte Differentialoperatoren hoeherer Ordnung, Proc. Int. Cong. Math. Amsterdam, Vol. II (1954), 243–250.
[S1] H. Sohrab,The C * -algebra of the n-dimensional harmonic oscillator, Manuscripta Math.34 (1981), 45–70.
[S2] H. Sohrab,A class of pseudo-differential C * -algebras, Quart. J. Math. Oxford40 (1989), 119–131.
[Tg1] T.-M. Tang,On C * -algebras related to Schroedinger type operators, Ph.D. Thesis, University of California, Berkeley, 1990.
[Tg2] T.-M. Tang,An algebra of singular integral operators on the half-line, to appear.
[Wi1] E. Wienholtz,Halbbeschraenkte partielle Differentialoperatoren zweiter Ordnung vom elliptischen Typus, Math. Ann.135 (1958), 50–80.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Shmuel Agmon
Rights and permissions
About this article
Cite this article
Cordes, H.O. On essential self-adjointness of powers and comparison algebras. J. Anal. Math. 58, 61–97 (1992). https://doi.org/10.1007/BF02790358
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02790358