双调和平面上的Schwartz型积分
Schwartz-type integrals in a biharmonic plane
摘要：
考虑复数域上的二维交换代数B。代数B与双调和方程有关。对于值在B中的单演函数，我们考虑了半平面和双调和平面圆盘上的Schwartz型边值问题（与主双调和问题相关）。我们通过Schwartz型积分得到了显式的解，并证明了上述问题对于半平面是无条件可解的，而对于圆盘是可解的当且仅当满足一定的自然条件。
英文摘要：
We consider a two-dimensional commutative algebra B over the field of complex numbers. The algebra B is associated with the biharmonic equation. For monogenic functions with values in B, we consider a Schwartz-type boundary value problem (associated with the main biharmonic problem) for a half-plane and for a disk of the biharmonic plane. We obtain solutions in explicit forms by means of Schwartz-type integrals and prove that the mentioned problem is solvable unconditionally for a half-plane but it is solvable for a disk if and only if a certain natural condition is satisfied.
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