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In my article (V. F. Zhdanovich, “Asymptotic expansions of eigenvalues of a boundary-value problem with a parameter”), published in *DAN*, vol. 135, no. 6, 1960, Theorem 3 in the formulation given in the article is incorrect. Since Theorem 4 partially relies on Theorem 3, Theorem 4 is not always true. Theorem 4 remains true if one additionally requires that representation (13) hold. In addition, in the formulation of Theorem 4, instead of the word “products” (p. 1321, line 8 from the top), one should read “derivatives.”
V. F. Zhdanovich
Submitted 1961-01-01 | RussiaRxiv: ru-196101.15315 | Translated from Russian

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In my article (V. F. Zhdanovich, “Asymptotic expansions of eigenvalues of a boundary-value problem with a parameter”), published in DAN, vol. 135, no. 6, 1960, Theorem 3 in the formulation given in the article is incorrect. Since Theorem 4 partially relies on Theorem 3, Theorem 4 is not always true. Theorem 4 remains true if one additionally requires that representation (13) hold. In addition, in the formulation of Theorem 4, instead of the word “products” (p. 1321, line 8 from the top), one should read “derivatives.”

V. F. Zhdanovich

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[v1] 1961-01-01

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In my article (V. F. Zhdanovich, “Asymptotic expansions of eigenvalues of a boundary-value problem with a parameter”), published in *DAN*, vol. 135, no. 6, 1960, Theorem 3 in the formulation given in the article is incorrect. Since Theorem 4 partially relies on Theorem 3, Theorem 4 is not always true. Theorem 4 remains true if one additionally requires that representation (13) hold. In addition, in the formulation of Theorem 4, instead of the word “products” (p. 1321, line 8 from the top), one should read “derivatives.”