## American Mathematical Society TranslationsTranslations of articles on mathematics appearing in various Russian mathematical serials. |

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### Contents

G Kreln Foundations of the theory of Xzones of stability of a canonical | 1 |

G Kreln On tests for stable boundedness of solutions of periodic | 71 |

A Jakubovii Critical frequencies of quasicanonical systems | 111 |

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### Common terms and phrases

absolutely continuous Akad assertion boundary boundary-value problem boundedness of solutions canonical equation canonical system characteristic value coincides corresponding Criterion critical frequencies definition denote direct sum dy/dt eigenvalues eigenvectors English transl equal equation 0.1 equation dx/dt equations with periodic formula G-unitary half-neighborhood hence Hermitian matrix implies inequality integral interval largest eigenvalue Lemma Lyapunov test matrix-valued function H(t modulus monodromy matrix Moreover multipliers of different nonnegative obtained orthogonal periodic coefficients perturbations point p0 positive eigenvalue positive type problem 6.1 Proof proposition quasicanonical systems real symmetric Russian scalar second kind skew-symmetric skew-symmetric matrix solutions of 0.8 stability of 0.2 stability of equation stable boundedness stable type stably bounded strong stability sufficiently small Suppose symmetric matrix symplectic matrix Theorem Theorem 4.1 theory unit circle unitary matrix value problem vector vector-valued function weakly stable Z-test zero zone of stability