Analogues of the V. I. Smirnov spaces for nonintegral exponents

Questions regarding the completeness and the minimality of systems of exponentials on curves are investigated. The analogues of the classical Hardy spaces are considered.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 115–127, 1988.     

Variable-stepsize Chebyshev-type methods for the integration of second-order I.V.P.'s

Panovsky and Richardson [A family of implicit Chebyshev methods for the numerical integration of second-order differential equations, J. Comput. Appl. Math. 23 (1988) 35–51] presented a method based on Chebyshev approximations for numerically solving the problem y^″=f(x,y)$y^{″}=f(x,y)$, being the steplength constant. Coleman and Booth [Analysis of a Family of Chebyshev Methods for y^″=f(x,y)$y^{″}=f(x,y)$, J. Comput. Appl. Math. 44 (1992) 95–114] made an analysis of the above method and suggested the convenience to design a variable steplength implementation. As far as we know this goal has not been achieved until now. Later on we extended the above method (this journal, 2003), and obtained a scheme for numerically solving the equation y^″-2gy^′+(g²+w²)=f(x,y)$y^{″}-2{\mathit{gy}}^{\prime }+(g^2+w^2)=f(x,y)$. The question of how to extend these formulas to variable stepsize procedures is the primary topic of this paper.     

An asymptotic formula for the mean value of the V. I. Arnold function

An asymptotic formula for the mean value of the V. I. Arnold function A(n) = \(\tfrac{{\sigma (n)}}{{\tau (n)}}\) is obtained, here σ(n) = \(\mathop \Sigma \limits_{d|n} \) d is the sum of all divisors of the number n, τ (n) = \(\mathop \Sigma \limits_{d|n} \) 1 is their quantity.     

Stability in the I. V. Ostrovskii-R. Cuppens theorem on groups

Let X be a locally compact separable metric Abelian group. Unimprovable estimates are obtained for the stability of the decompositions of the generalized Poisson distribution e(F) on X, where F is a completely finite measure on X such that its powers f^n* with respect to convolution are pairwise singular for distinct natural numbers n.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 103–108, 1988.     

Sufficient and necessary conditions for limit laws on lag sums of I. I. D. R. V. S

Let {X, X _n ;n>-1} be a sequence of i.i.d.r.v.s withEX=0 andEX ²=σ²(0 < σ < ∞). we obtain some sufficient and necessary conditions for

Factorization of probability distributions from Yu. V. Linnik's class L. I

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 47, pp. 3–25, 1987.     

A counterexample to the hypothesis of V. I. Arnol'd regarding the proper vibrations of the membrane

It is shown that the hypothesis of transversality formulated by V. I. Arnol'd is not satisfied for all domains. Examples are presented of domains for which the variations of the eigenvalues of the Laplace operator for small perturbations of the domain are linearly dependent.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 51, pp. 134–137, 1975.     

The Petersson conjecture for the weight zero. I

In the present paper, a known result by Eichler-Deligne concerning the Petersson conjecture for finite-dimensional classical spaces is proved for infinite-dimensional Hilbert spaces of weight 0. In this work, the techniques of spectral decompositions of convolutions are used. The work is divided into two parts. In this (first) part, an explicit representation of an eigenvalue of the Hecke operator in terms of the spectral components of the convolution is obtained. On the basis of this representation, the Petersson conjecture will be proved in the second part. Bibliography: 9 titles. Dedicated to O. A. Ladyzhenskaya Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 249, 1997, pp. 118–152. Translated by N. A. Karazeeva.     

均值误差的随机加权逼近的重对数律──非独立同分布情况

讨论了独立不同分布情况下均值误差的分布估计问题,用随机加权法给出了精度为O(√lnlnn/n)的逼近分布.     

The Problem of V. N. Dubinin for Symmetric Multiconnected Domains

Ukrainian Mathematical Journal - We consider a quite general problem from the geometric theory of functions, namely, the problem of finding the maximal value of the product of inner radii of n...     

Applications of coordinatization in modular lattice theory: The legacy of J. von Neumann

This paper reviews current work based on von Neumann's coordinization theorem.     

The V. A. Steklov problem in the theory of orthogonal polynomials

An exact order of growth of Szego polynomial kernels and moduli of polynomials orthogonal in the unit circle is obtained in the zeros of a weight function of special form. Other questions are also examined.