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.     

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.     

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.     

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

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.     

On a theorem of V. V. Filippov

A new characterization of spaces having a point-countable basis is obtained. This characterization is used in giving a simpler proof of a recent theorem of Filippov. Partly supported by an N.S.F. grant.     

Optimal rate of convergence of V. I. Lebedev's method on some classes of operator equations

Upper and lower estimates are obtained for the rate of convergence of V. I. Lebedev's method on certain classes of operator equations of the second kind.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 541–547, April, 1992.     

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.