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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

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