• Journal of applied mathematics & informatics
• /
• v.40 no.1_2
• /
• pp.173-184
• /
• 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
• /
• v.10 no.1
• /
• pp.35-45
• /
• 1994

• Kyungpook Mathematical Journal
• /
• v.32 no.3_spc
• /
• pp.421-434
• /
• 1992

• Kyungpook Mathematical Journal
• /
• v.30 no.1
• /
• pp.1-6
• /
• 1990

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.411-418
• /
• 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].

• Communications of the Korean Mathematical Society
• /
• v.10 no.4
• /
• pp.907-916
• /
• 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 $0 < r < 1$.