Abstract
We extend expansion results of [2,3] on nonuniformly right definite multi-parameter problems. We also obtain an abstract approximation criterion for the existence of commuting self-adjoint extensions of a family of symmetric operators.
Research supported in part by the FFR of Ukraine Grant 1/238 “Operator”
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Yu.M. Berezansky, “Expansions in Eigenfunctions of Self-Adjoint Operators”, Translations of Mathematical Monographs, Vol.17, Amer. Math. Soc, Providence, RI, 1968.
Yu.M. Berezansky and A.Yu. Konstantinov, On eigenvector expansion of multi-parameter spectral problems, Funk.Anal, i Ego Pril. 26, No. 1 (1992), 81–83.
Yu.M. Berezansky and A.Yu. Konstantinov, Expansion in eigenvectors of multiparameter spectral problems, Ukr.Mat.J. 44, No. 7 (1992), 901–913.
P. Binding, Nonuniform right defmiteness, J. Math. Anal. Appl. 102 (1984), 233–243.
P.J. Browne, A singular multi-parameter eigenvalue problem in second order ordinary differential equations, J. Differential Equations 12 (1972), 81–94.
H.A. Isaev, On singular multiparameter differential operators, Mat. Sbornik, 131, No.1 (1986), 52–72.
H. Volkmer, On multiparameter theory, J. Math. Anal. Appl. 86 (1982), 44–53.
H. Volkmer, “Multiparameter Eigenvalue Problems and Expansion Theorems”, Springer-Verlag, Berlin-New-York, 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Basel AG
About this chapter
Cite this chapter
Konstantinov, A. (1994). Eigenfunction expansion of right definite multiparameter problems. In: Demuth, M., Exner, P., Neidhardt, H., Zagrebnov, V. (eds) Mathematical Results in Quantum Mechanics. Operator Theory: Advances and Applications, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8545-4_39
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8545-4_39
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9673-3
Online ISBN: 978-3-0348-8545-4
eBook Packages: Springer Book Archive