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八○年国际天线与传播会议上,我国学者陈敬熊老师发表了一篇富有创见的论文。他用算子理论推导了园口径最高方向性分布所满足的方程,并且表示出了这个方程的解,证明了相应的方向性是无穷大。由于通常口径上的能量总是有限的,因此本文试图进一步研究这个方程的解是否属于L~2空间[注1]。本文将从研究线源入手,先推导有相线源和同相线源的最高方向性分布分别所满足的方程。然后证明有相线源的最高方向性分布不属于L~2空间,即在L~2空间内有相线源不存在最高方向性分布。最后,把此结果推广到园口径情况。
During the 80th International Conference on Antennas and Propagation, our scholar Professor Chen Jingxiong published a brilliant essay. Using operator theory, he deduces the equation satisfied by the highest directivity distribution of the park caliber and expresses the solution of this equation, proving that the corresponding directivity is infinite. Since the caliber of energy is usually finite, this paper attempts to further investigate whether the solution of this equation belongs to L ~ 2 space [1]. This article will start with the study of line sources, first derive the equations that the highest directivity distributions of phase source and in-phase source meet respectively. Then it is proved that the highest directivity distribution of phase source does not belong to L ~ 2 space, that is, there is no highest directivity distribution in phase space source in L ~ 2 space. Finally, this result is extended to the park caliber situation.