关于有限卷积与微分算子的交换性质I：交换
On the commutation properties of finite convolution and differential operators I: commutation
摘要：
许多有限卷积积分算子的谱性质已经通过寻找与它们可交换的微分算子而得到了理解。在本文中，我们编制了一个完整的列表，这样的交换对，扩展以前的工作，复值和非自伴算子。此外，我们引入了一种新的交换关系，我们称之为sesquicommutation，这也有影响的积分算子的谱特性。在这种情况下，我们也计算一个完整的列表sequiccommuting对的积分和微分算子。
英文摘要：
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to complex-valued and non self-adjoint operators. In addition, we introduce a new kind of commutation relation, which we call sesquicommutation, that also has implications for the spectral properties of the integral operator. In this case we also compute a complete list of sequicommuting pairs of integral and differential operators.
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