A multidimensional analog of a theorem due to zygmund

Zygmund proved an inequality describing the dependence of the modulus of continuity of the adjoint function on that of the original function lying in the space of 2π-periodic continuous functions. The present article contains estimates of partial moduli of continuity of the adjoint function of several variables in the spaceC. Examples show that these estimates are sharp. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 717–727, May, 1997. Translated by A. M. Chebotarev     

On a combinatorial theorem related to a theorem of G. Szegö

In 1954, M. Kac discovered a probabilistic interpretation of a theorem of G. Szegö of Toeplitz matrices and demonstrated that this theorem can be provedin an elementary way by using a combinatorial identify of G. A. Hunt. In this paper Hunt's combinatorial identity is derived from a more general combinatorial result.     

On a density theorem

Translated from Matematichskie Zametki, Vol. 51, No. 6, pp. 32–40, June, 1992.     

On a Kleinecke-Shirokov theorem

Czechoslovak Mathematical Journal - We prove that for normal operators N1, $${N_2} \in {\cal L}({\cal H})$$ , the generalized commutator [N1, N2; X] approaches zero when [N1, N2; [N1, N2; X]] tends...     

On a comparison theorem

This paper gives a generalization of the Sturm comparison theorem for differential equations (p): y″ = p(t)y, (q): y″ = q(t)y under the assumption that the function p ? q changes its sign exactly once on [a, b] or ∝_t^bp ? q, ∝_a^tp ? q maintain the sign on [a, b]. The results are used for investigating the distributions of zeros of solutions and the derivative of solutions of (p), (q).     

On a minimax theorem

The aim of this note is to prove the following statement. It gives an extension of the theorem proved by O. Y. Borenshtein and V. S. Shul'man in [1].     

ON A MIN-MAX THEOREM

In this paper we prove a nonvariational form of a rain-max problem in [l] and give its application to a periodical problem.     

On a theorem relating to the mutiple thetafunctions

Ohne Zusammenfassung

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On a theorem relating to the mutiple thetafunctions

     

On a fixed-point theorem

Institute of Mathematics, Hanoi. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 30, No. 3, pp. 93–94, July–September, 1996.     

On the Skitovich-Darmois theorem and Heyde theorem in a Banach space

According to the well-known Skitovich-Darmois theorem, the independence of two linear forms of independent random variables with nonzero coefficients implies that the random variables are Gaussian variables. This result was generalized by Krakowiak for random variables with values in a Banach space in the case where the coefficients of forms are continuous invertible operators. In the first part of the paper, we give a new proof of the Skitovich-Darmois theorem in a Banach space. Heyde proved another characterization theorem similar to the Skitovich-Darmois theorem, in which, instead of the independence of linear forms, it is supposed that the conditional distribution of one linear form is symmetric if the other form is fixed. In the second part of the paper, we prove an analog of the Heyde theorem in a Banach space. Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1234–1242, September, 2008.     

On a theorem by Brewer

One of the most frequently referenced monographs on power series rings, “Power Series over Commutative Rings” by James W. Brewer, states in Theorem 21 that if M is a non-SFT maximal ideal of a commutative ring R with identity, then there exists an infinite ascending chain of prime ideals in the power series ring $R?X?$, $Q_0?Q_1???Q_n??$ such that $Q_n\cap R=M$ for each n. Moreover, the height of $M?X?$ is infinite. In this paper, we show that the above theorem is false by presenting two counter examples. The first counter example shows that the height of $M?X?$ can be zero (and hence there is no chain $Q_0?Q_1???Q_n??$ of prime ideals in $R?X?$ satisfying $Q_n\cap R=M$ for each n). In this example, the ring R is one-dimensional. In the second counter example, we prove that even if the height of $M?X?$ is uncountably infinite, there may be no infinite chain $\{Q_n\}$ of prime ideals in $R?X?$ satisfying $Q_n\cap R=M$ for each n.     

On a theorem of yulmukhametov

A new version and a modified proof of Yulmukhametov’s theorem on the decomposition of measures are given. Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 859–862, June, 2000.     

On a theorem of gordin

M. I. Gordin proved a central limit theorem for some strictly stationary strongly mixing random sequences without the usual assumption of finite second moments. In this note we show that in that theorem, his assumption of a mixing rate (for the strong mixing condition) cannot be altogether omitted     

On a theorem of camillo

Let R denote a right principally injective ring. In this note we show that if R is right duo then R is right finite dimensional if and only if R has a finite number of maximal left ideals. This extends and answers an open question of Camillo. If, instead, every simple right module can be embedded in R, we show that R is left finite dimensional if it has a finite number of maximal right ideals.