Subnormal generalized Hausdorff operators
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- by B. K. Ghosh, B. E. Rhoades and D. Trutt PDF
- Proc. Amer. Math. Soc. 66 (1977), 261-265 Request permission
Abstract:
One type of generalized Hausdorff matrix is the lower triangular matrix with entries ${h_{nk}} = (_{n - k}^{n + \alpha }){\Delta ^{n - k}}{\nu _k}$, where $\Delta {\nu _n} = {\nu _n} - {\nu _{n + 1}},{\nu _n} = \smallint _0^1{t^{n + \alpha }}d\beta (t)$ for some $\beta (t)$ of bounded variation on [0, 1] and for some $\alpha \geqslant 0$. The matrix ${H_\alpha }$ generated by ${\nu _n} = {(n + \alpha + 1)^{ - 1}}$ is shown to be a subnormal operator on ${l^2}$ if $\alpha$ is a nonnegative integer.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 261-265
- MSC: Primary 40C05; Secondary 47B20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0467068-5
- MathSciNet review: 0467068