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The Spectra of Semi-Normal Singular Integral Operators

Published online by Cambridge University Press:  20 November 2018

C. R. Putnam
C. R. Putnam*
Affiliation:
Purdue University, Lafayette, Indiana
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Suppose that

(1.1)

and define the bounded self-adjoint operators H and J on the Hilbert space L2(0, 1) by

(1.2)

the integral being a Cauchy principal value

It is seen that

(1.3)

or, equivalently,

(1.4)

Since (Cƒ, ƒ) = π–1|(ƒ, ϕ)|2 ≧ 0, A is semi-normal. (For a discussion of such operators, see [4].)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 1 , 01 February 1970 , pp. 134 - 150
Copyright
Copyright © Canadian Mathematical Society 1970

References

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