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 the method of infrared spectra,” published in DAN, 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 the numbers of the curves should be changed: 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. Byalykh and S. E. Severin, “Labile phosphorus compounds of the heart muscle of rabbits in aortic stenosis”), published in DAN, vol. 136, no. 2, 1961, in the text where data are given on the content of labile phosphorus in electrophoretic fractions, instead of the indicated mg-%, it should read μg.

M. F. Byalykh, S. E. Severin

In my article (A. L. Zelmanov, “On the question of the deformation of the concomitant space in Einstein’s theory of gravitation”), published in DAN, 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As has become known to us, in the unpublished doctoral dissertation of M. S. Livshits, “On mirror-conjugate and self-adjoint extensions of symmetric operators forming a simple system, and on some of their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 was studied: that of extending a positive-definite function, defined in a convex centrally symmetric domain, to the whole space; 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 has 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 a development 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 the general definition of M. G. Krein for a convex centrally symmetric domain (formula (5)), a misprint was made: in (5) the sides of the rectangle should be reduced by half.

R. Ismagilov
G. Eskin

References Cited

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