Completely seminormal operators with boundary eigenvalues
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- by Kevin Clancey PDF
- Trans. Amer. Math. Soc. 182 (1973), 133-143 Request permission
Abstract:
For $f \in {L^2}(E)$ we consider the singular integral operator ${T_E}f(s) = sf(s) + {\pi ^{ - 1}}{\smallint _E}f(t){(t - s)^{ - 1}}dt$. These singular integral operators are a special case of operators acting on a Hilbert space with one dimensional self-commutator. We discover generalized eigenfunctions of the equation ${T_E}f = 0$ and, for $p < 2$, we will give an ${L^p}(E)$ solution of the equation ${T_E}f = {\chi _E}$. The main result of the paper is an example of a nonzero ${L^2}(E)$ solution of ${T_E}f = 0$, with $\lambda = 0$ a boundary point of the spectrum of ${T_E}$.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 182 (1973), 133-143
- MSC: Primary 47B37
- DOI: https://doi.org/10.1090/S0002-9947-1973-0341167-1
- MathSciNet review: 0341167