• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.173-184
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• 2022

We investigated the invariant subspaces of the fractional integral operator in the Sobolev space W^k_p[0, 1] and prove unicellularity of the operator J^α by using the Duhamel product.

• East Asian mathematical journal
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• 제10권1호
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• pp.35-45
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• 1994

• Kyungpook Mathematical Journal
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• 제32권3_spc호
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• pp.421-434
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• 1992

• Kyungpook Mathematical Journal
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• 제30권1호
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• pp.1-6
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• 1990

• 대한수학회보
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• 제37권3호
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• pp.411-418
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• 2000

In this paper, we want to give an operator which is not unicellular. We try to prove the non-unicellularity of the operator by using the method given in [8].

• 대한수학회논문집
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• 제10권4호
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• pp.907-916
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• 1995

The unilateral weighted shift operator $W_r$ with the weighted sequence ${r^n}^\infty_{n=0}$ is unicellular if $0 < r < 1$. In general, A + B is not unicellular even if A and B are unicellular. We will prove that $W_r + W^2_r$ is unicellular if $0 < r < 1$.