Corrections to the Article “On Estimates of Integral Norms of Eigenfunctions of the Laplace Operator in Certain Domains” (Doklady, Vol. 183, No. 1, 1968)
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Corrections
In my article (Li Hoang Tu, “An Approximate Minimal Property of the \(R^2\) Test”), published in DAN, vol. 180, no. 4, 1968, the following corrections must be made:
On p. 793, line 2 from the bottom, printed:
\[ O\left(\lambda/N^k\right) \leq \alpha \leq \lambda - O\left(1/\ln N\right) \tag{2} \]
should read:
\[ O\left(1/N^k\right) \leq \alpha \leq 1 - O\left(1/\ln N\right). \tag{2} \]
On p. 793, line 1 from the bottom, printed:
\[ 1/N\ln N \leq \delta \leq 1 \]
should read:
\[ 1/N\ln N \leq \delta < 1. \]
On p. 794, line 14 from the bottom, printed:
\[ \frac{1}{N}\ln N \leq \delta \leq \frac{12K\ln n}{N}; \qquad \frac{2}{\ln N} \leq C \leq \frac{2K\ln n}{N} \]
should read:
\[ \frac{1}{N}\ln N \leq \delta \leq \frac{12k\ln N}{N}; \qquad \frac{2}{\ln N} \leq C \leq \frac{12k\ln N}{N}. \]
Li Hoang Tu
In the article by M. L. Goldman, “On Estimates of Integral Norms of Eigenfunctions of the Laplace Operator in Some Domains,” published in vol. 183, no. 1, 1968:
| Printed | Should read | |
|---|---|---|
| P. 21, 4th line from the bottom | \(q > 2\) | \(q \geq 1\) |
| P. 24, 6th line | \(\displaystyle \lim_{n}\left\|u_n(x)\right\|_{L_1(g)} > 0\) | \(\displaystyle \lim_{n}\left\|u_n(x)\right\|_{L_1(g)} > 0\) |
| 15th line | \(\displaystyle \lim_{n}\left\|u_n(x)\right\|_{L_q} = \infty\) | \(\displaystyle \lim_{n}\left\|u_n\right\|_{L_q} = \infty\) |