Abstract
We develop spectral and scattering theory for one class of self-adjoint matrix operators of mixed order.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. V. Atkinson, H. Langer, R. Mennicken, and A. A. Shkalikov, “The essential spectrum of some matrix operators,” Math. Nachr., 167, 5–20 (1994).
A. A. Shkalikov, “On the essential spectrum of matrix operators,” Mat. Zametki, 58, 945–949 (1995).
M. Faierman, R. Mennicken, and M. Möller, “A boundary eigenvalue problem for a system of partial differential operators occurring in magnetohydrodynamics,” Math. Nachr., 173, 141–167 (1995).
H. Langer and M. Möller, “The essential spectrum of a nonelliptic boundary-value problem,” Math. Nachr., 178, 233–248 (1996).
A. Yu. Konstantinov, “Spectral and scattering theory of some matrix operators related to Schrödinger equations with potentials depending rationally on the spectral parameter,” Meth. Function. Anal. Topology, 2, No. 3, 4, 69–77 (1996).
A. Yu. Konstantinov, “Spectral analysis of one class of matrix differential operators,” Function, Anal. Appl., 31, No. 3, 209–211 (1997).
V. Adamyan, H. Langer, R. Mennicken, and J. Saurer, “Spectral components of self-adjoint block operator matrices with unbounded entries,” Math. Nachr., 178, 43–80 (1996).
R. Mennicken and A. A. Shkalikov, “Spectral decomposition of symmetric operator matrices,” Math. Nachr., 179, 259–273 (1996).
V. Adamyan and H. Langer, “Spectral properties of a class of rational operator valued functions,” J. Oper. Theory, 33, 259–277 (1995).
E. Mourre, “Absence of a singular continuous spectrum for certain self-adjoint operators,” Commun. Math. Phys., 78, 391–408 (1981).
P. A. Perry, I. M. Sigal, and B. Simon, “Spectral analysis of N-body Schrödinger operators,” Ann. Math., 114, 519–567 (1981).
W. Amrein, A. Boutet de Monvel, and V. Georgescu, C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, Birkhäuser, Basel (1996).
A. Boutet de Monvel, V. Georgescu, and M. Mantoiu, “Locally smooth operators and the limiting absorption principle for N-body Hamiltonians,” Rev. Math. Phys., 5, No. 1, 105–189 (1993).
A. Boutet de Monvel-Berthier and V. Georgescu, “Spectral and scattering theory by the conjugate operator method,” Alg. Analiz, 4, No. 3, 79–116 (1992).
D. R. Yafaev, “Remarks on spectral theory for multiparticle Schrödinger operators,” Zap. Nauchn. Sem. LOMI, 133, 277–298 (1984).
Author information
Authors and Affiliations
Additional information
Published in Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1064–1072, August, 1998.
Rights and permissions
About this article
Cite this article
Konstantinov, A.Y. Spectral theory of some matrix differential operators of mixed order. Ukr Math J 50, 1212–1223 (1998). https://doi.org/10.1007/BF02513093
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02513093