Corrections

In the article by Yu. M. Berezanskii, “Generalization of Bochner’s theorem to expansions in eigenfunctions of partial differential equations,” published in DAN, vol. 110, no. 6, 1956, after formula (1) one should read: with complex-valued coefficients; \(L'\) will denote the expression conjugate to \(L\), and \(\overline L\) the expression obtained from \(L\) by replacing the coefficients with their complex conjugates. In the case of ordinary derivatives we shall assume that the coefficients \(a_{k_1}(x)\) are \(2 + k_1\) times continuously differentiable; in the case of partial derivatives, that \(a_{k_1,\ldots,k_n}(x)\) are \(2n + r + k_1 + \cdots + k_n\) times continuously differentiable, and that \(L\), together with the expression \(\mathscr{L}'[F] = L_x[F] + \overline L_y[F]\) \((F = F(x,y))\), is elliptic*.

In the article by N. P. Movchan, “The influence of anelectrotonus on inhibited positive conditioned reflexes,” published in DAN, vol. 112, no. 6, 1957: