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On a Class of Non-Self-Adjoint Differential Operators

Published online by Cambridge University Press:  20 November 2018

R. R. D. Kemp
R. R. D. Kemp*
Affiliation:
Queen's University
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The problem of spectral analysis of non-self-adjoint (and non-normal) operators has received considerable attention recently. Livšic (5), and more recently Brodskii and Livšic (1) have considered operators on Hilbert space with completely continuous imaginary parts. Dunford (3) has generalized the notion of spectral measure and defined a class of spectral operators on Hilbert and Banach space. Schwartz (8) and Rota (7) have investigated conditions under which a differential operator will be spectral. The work of Naimark (6) and the author (4) on non-self-adjoint differential operators leads to an expansion theorem which implicitly defines a type of spectral measure. However the projections involved in this will not in general be bounded, much less uniformly bounded.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 641 - 659
Copyright
Copyright © Canadian Mathematical Society 1960

References

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