Corrections to the Article “The Riemann–Hilbert Problem for a Holomorphic Vector” (Doklady, Vol. 126, No. 4, 1959)

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Submitted 1960 | SovietRxiv: ru-196001.90927 | Translated from Russian

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BIOCHEMISTRY

I. P. Kok. The effect of propylgallate on the concentration of nucleic acids in healthy and virus-infected Pupae of Antheraea pernyi G.-M. — 1141

W. L. Kretovich and E. Galas. Synthesis of aminoacids from oxalacetic and pyruvic acids in barley seedlings — 1144

L. B. Mekler, N. N. Lapteva, D. V. Lozovskii and T. I. Balezina. On chemical and biological properties of taraxein — a toxic protein observed in the blood serum of schizophrenic patients — 1148

PLANT ANATOMY

I. N. Polukhina. On the mode of internode growth in wheat and rye — 1152

PLANT EMBRYOLOGY

M. I. Savchenko. Anomalies in the structure of the seed-bud in Angiosperms — 1154

PLANT PHYSIOLOGY

B. I. Eskin. Anthocyanin and frost resistance of plants — 1158

ZOOLOGY

V. E. Sidorov. On the nature of coxal liquor in Ornithodoros lahorensis, O. papillipes and Argas persicus — 1161

EXPERIMENTAL MORPHOLOGY

L. V. Belousov and Tsegmid Gheleg. Chemical control of morphogenesis in hydroid polyps — 1165

N. A. Verzhbinskaia. On the tissue mechanism of the adaptation of animals to hypoxia — 1169

EMBRYOLOGY

L. I. Radzinskaia. The peroxidase reaction and hemoglobin formation in the course of embryogenesis in Acipenseridae — 1173

ERRATUM

In my paper “The Riemann–Hilbert Problem for a Holomorphic Vector,” published in DAN, vol. 126, no. 4, 1959, in the definition of the class of quasi-diagonal matrices \(\Lambda\), a series of “elementary cells” of the form

\[ \left( \begin{array}{cc} z^{\chi_1}, & iz^{\chi_2}\psi_k(z)\\ 0, & z^{\chi_2} \end{array} \right), \qquad \text{where }\psi_k(z)=\frac{1+z-2z^{k+1}}{1-z} \quad (D \text{ is the disk } |z|<1), \]

was omitted, where \(\chi_1\) and \(\chi_2\) are the partial indices of the cell, \(k=\chi_1-\chi_2-1>0\). In connection with this, the corollary to Theorem 1 is incorrect, and the formula for \(l(A)\) takes the form

\[ l=\sum_i (2|\chi_{r_i}|+1)+\sum_j 2|\chi_{\rho_j}|, \]

where \(\chi_{r_i}\) are all free partial indices, \(\chi_{r_i}\leqslant 0\), or those coupled indices \((\chi_{r_i},\chi_{r_i+1})\) for which \(\chi_{r_i}\leqslant 0,\ \chi_{r_i+1}<0\), and \(\chi_{\rho_j}\) are the remaining negative partial indices. Theorem 1 is valid if \(\Lambda\) is understood in the indicated extended sense. The remaining theorems remain unchanged.

B. Boyarskii

T-00417. Signed for printing 4/II 1960. Print run 5100 copies. Order no. 2518.
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Submission history

Corrections to the Article “The Riemann–Hilbert Problem for a Holomorphic Vector” (Doklady, Vol. 126, No. 4, 1959)