BIOCHEMISTRY
S. S. Vasileiskii. A chromatographic study of the dialyzed hemopoietic factor of the stomach ..... 1460
I. D. Ivanov. The polarographic wave, and the enzymatic activity of proteinases ..... 1463
V. A. Iakovlev, E. V. Rosengart. The effect of esterase reduced to a model ..... 1467

PLANT PHYSIOLOGY
T. A. Danilova, E. N. Davydova. On the effect of cobalt on plants ..... 1470

ZOOLOGY
Iu. V. Natochin, V. V. Khlebovich, T. V. Krestinskaia. Succindehydrase in sodium transporting organs of invertebrates ..... 1474

EXPERIMENTAL MORPHOLOGY
I. S. Darevskii. The evolution of eyelid concrescence in lizards ..... 1477
Iu. A. Fedorov. The effect of phosphorus-calcium and fluorine compounds on experimental caries in white rats ..... 1481

EVOLUTIONAL MORPHOLOGY
V. D. Il’ichev. The morphological and functional peculiarities of the external ear in birds characterized by crepuscular or nocturnal mode of life ..... 1485

LETTER TO THE EDITOR

Having re-examined my note “On the impossibility of constructing a linear polynomial operator giving an approximation of the order of the best” (¹), I found that the method of proof of Theorems 1 and 2 makes it possible, without any additions, to obtain a considerably more interesting theorem, which, in the notation and terminology of the note mentioned, is formulated as follows:

Theorem. In order that, for a functional space of type \(E\), it be possible to construct a sequence of linear trigonometric polynomial operations \(U_n(f,x)\), \(n=1,2,\ldots\), giving an approximation of the order of the best, it is necessary and sufficient that for every \(f\in E\) the equality

\[ \| f - S_n(f) \| = O(E_n), \quad n=1,2,\ldots, \]

hold, where \(S_n(f)\) is the partial sum of the Fourier series of the function \(f(x)\) of order \(n\), and \(E_n\) is the best approximation of \(f(x)\) by means of a polynomial of order \(n\) in the metric of the space \(E\).

We note that the theorem remains valid for a certain more general class of functional spaces, and also for the case of harmonic analysis on bicompact commutative topological groups.

D. Berman

REFERENCES CITED

¹ D. Berman, DAN, 120, No. 6 (1958).