2.—Semi-bounded Second-order Differential Operators
2.—Semi-bounded Second-order Differential Operators
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2.—半有界二阶微分算子
DOI：
10.1017/s0080454100009377
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发表时间：
1974
期刊：
影响因子：
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通讯作者：
M. Eastham
中科院分区：
文献类型：
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作者：
M. Eastham
考虑L2（0,∞）上由微分表达式My(x) = -y″(x)+q(x)y(x)生成的微分算子。假设对于[0，∞)内的所有x和某个固定的ω > 0都是有界的。这些算子在下面是有界的，并且用q(x)得到了下界的估计。对于某p≧1，当q(x) = LP（0,∞）时，将结果与W. N. Everitt最近的结果进行了比较。对结果的最佳性质进行了一些评论。
Synopsis Differential operators generated by the differential expression My(x) = —y″(x)+q(x)y(x) in L2(0, ∞) are considered. It is assumed that is bounded for all x in [0, ∞) and some fixed ω > 0. The operators are shown to be bounded below and an estimate for the lower bound is obtained in terms of q(x). In the case where q(x) is LP (0, ∞) for some p ≧ 1, the results are compared with recent ones of W. N. Everitt. Some comments are made on the best-possible nature of the results.