Corrections

In our article (A. N. Rodionov, T. V. Talalaeva, D. N. Shigorin, and K. A. Kocheshkov, “Investigation of the Structure of Complexes of Organolithium Compounds with Simple Ethers by Infrared Spectra”), published in Dokl. Akad. Nauk, vol. 136, no. 2, 1961, the following corrections must be made:

a) the captions to Figs. 1B and 1A should be interchanged;

b) in spectrum 1B, change the numbers of the curves: instead of 2 there should be 1; instead of 3—2; and instead of 1—3.

A. N. Rodionov, T. V. Talalaeva, D. N. Shigorin, K. A. Kocheshkov

In our article (M. F. Vyalykh and S. E. Severin, “Labile Phosphorus Compounds of Rabbit Heart Muscle in Aortic Stenosis”), published in Dokl. Akad. Nauk, vol. 136, no. 2, 1961, in the text where the data on the content of labile phosphorus in electrophoretic fractions are given, instead of the stated mg-%, it should read μg.

M. F. Vyalykh, S. E. Severin

In my article (A. L. Zelmanov, “On the Question of the Deformation of the Accompanying Space in Einstein’s Theory of Gravitation”), published in Dokl. Akad. Nauk, vol. 135, no. 6, 1960, on p. 1370, in line 24, the equality $\partial^2(\omega_1\omega_2\omega_3)/(\partial x^0)^2 = 0$ should be deleted; in line 25, delete “(for the same $x^i$).”

Letter to the Editor

As has become known to us, in the unpublished doctoral dissertation of M. S. Livshits, “On mirror-conjugate and self-adjoint extensions of symmetric operators forming a simple system, and on some of their applications” (¹), the problem posed by M. G. Krein of extending a positive-definite function given in a convex centrally symmetric domain to the whole space was studied; this problem is connected with the problem of commuting extensions of a system of symmetric operators.

Our notes (², ³) are devoted to this same question. As it turned out, Theorem 5 in (²) and Theorem 3 in (³) were first proved by M. S. Livshits in (¹). In (¹) there is also proved a general theorem on the existence of commuting extensions of two symmetric operators, one of which is self-adjoint, using an involution, so that Theorem 1 in (²) and Theorem 1 in (³) may be regarded as developments of this theorem of M. S. Livshits. In addition, in the definition of a positive-definite function in (³), which is a special case of M. G. Krein’s general definition for a convex centrally symmetric domain (formula (5)), an error was made: in (5) the sides of the rectangle must be reduced by half.

R. Ismagilov
G. Eskin

Cited Literature

1. M. S. Livshits, Doctoral dissertation, Bayram-Ali, 1944.
2. R. S. Ismagilov, Dokl. Akad. Nauk 133, no. 3, 511 (1960).
3. G. I. Eskin, Dokl. Akad. Nauk 133, no. 3, 540 (1960).