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Multiparameter root vectors

Published online by Cambridge University Press:  20 January 2009

Paul Binding
Paul Binding
Affiliation:
Department of Mathematics and StatisticsUniversity of CalgaryCalgary, AlbertaCanadaT2N IN4
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The concept of “root vectors” is investigated for a class of multiparameter eigenvalue problems

where operate in Hilbert spaces Hm and . Previous work on this “uniformly elliptic” class has demonstrated completeness of the decomposable tensors x1 ⊗…⊗ xk in a subspace G of finite codimension in H=H1 ⊗…⊗ Hk, but questions remain about extending this to a basis of H. In this work, bases of elements ym, in general nondecomposable but satisfying recursive equations of the type are constructed for the “root subspaces” corresponding to λ∈ℝk.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 1 , February 1989 , pp. 19 - 29
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

1.Atkinson, F. V., Multiparameter spectral theory, Bull. Amer. Math. Soc. 74 (1968), 1–27.CrossRefGoogle Scholar
2.Atkinson, F. V., Multiparameter Eigenvalue Problems Vol. 1 (Academic Press, 1972).Google Scholar
3.Binding, P. A., Multiparameter definiteness conditions, Proc. Roy. Soc. Edinburgh 89A (1981), 319–332.CrossRefGoogle Scholar
4.Binding, P. A., Left definite multiparameter eigenvalue problems, Trans. Amer. Math. Soc. 272 (1982), 476–486.CrossRefGoogle Scholar
5.Binding, P. A. and Browne, P. J., Applications of two parameter spectral theory to symmetric generalised eigenvalue problems, preprint.Google Scholar
6.Binding, P. A. and Seddighi, K., On root vectors for self-adjoint pencils, J. Funct. Anal. 70 (1987), 117–125.CrossRefGoogle Scholar
7.Binding, P. A. and Seddighi, K., Elliptic multiparameter eigenvalue problems, Proc. Edinburgh Math. Soc. 30 (1987), 215–228.CrossRefGoogle Scholar
8.Faierman, M., Expansions in eigenfunctions of two-parameter system of differential equations I–IV, preprints.Google Scholar
9.Gadzhiev, G. A., On a mullidme equation and its reduction to a multiparameter spectral problem, Soviet Math. Dokl. 32 (1985), 710–713.Google Scholar
10.Isaev, G. A., On root elements of multiparameter spectral problems, Soviet Math. Dokl. 21 (1980), 127–130.Google Scholar
11.Kallstrom, A. and Sleeman, B. D., Solvability of a linear operator system, J. Math. Anal. Appl. 55 (1976) 785–793.CrossRefGoogle Scholar
12.Kallstrom, A. and Sleeman, B. D., A left definite multiparameter eigenvalue problem in ‘ordinary differential equations, Proc. Roy. Soc. Edinburgh 74A (1976), 145–155.CrossRefGoogle Scholar
13.Kato, T., Perturbation Theory for Linear Operators (Springer-Verlag, 1976).Google Scholar