Abstract: In this paper we obtain a sufficient condition for quite continuity of Fredholm type integral operators in the space L1(a, b). Uniform approximations by operators with degenerate kernels of horizontally striped structures are constructed. A quantitative error estimate is obtained. We point out the possibility of application of the obtained results to second kind integral equations, including convolution equations on a finite interval, equations with polar kernels, one-dimensional equations with potential type kernels, and some transport equations in non-homogeneous layers. PubDate: 2018-11-01 DOI: 10.3103/S106836231806002X
Abstract: The problem of the sine representation for the support function of centrally symmetric convex bodies is studied. We describe a subclass of centrally symmetric convex bodies which is dense in the class of centrally symmetric convex bodies. Also, we obtain an inversion formula for the sine-transform. PubDate: 2018-11-01 DOI: 10.3103/S1068362318060079
Abstract: In this paper, we show that the norm of the Bergman projection on Lp,q-spaces in the upper half-plane is comparable to csc(π/q). Then we extend this result to a more general class of domains, known as the homogeneous Siegel domains of type II. PubDate: 2018-11-01 DOI: 10.3103/S1068362318060031
Abstract: In this paper, we prove that for any ε ∈ (0, 1) there exists ameasurable set E ∈ [0, 1) with measure E > 1 − ε such that for any function f ∈ L1[0, 1), it is possible to construct a function \(\tilde f \in {L^1}[0,1]\) coinciding with f on E and satisfying \(\int_0^1 { \tilde f(x) - f(x) dx < \varepsilon } \) , such that both the Fourier series and the greedy algorithm of \(\tilde f\) with respect to a bounded Vilenkin system are almost everywhere convergent on [0, 1). PubDate: 2018-11-01 DOI: 10.3103/S1068362318060043
Abstract: The paper gives the delta-subharmonic extension of the part of the factorization theory of M. M. Djrbashian - V. S. Zakaryan, which relates with the descriptive representations of the classes N{ω} of functions meromorphic in the unit disc, contained in Nevanlinna’s class N of functions of bounded type. PubDate: 2018-11-01 DOI: 10.3103/S1068362318060055
Abstract: The paper considers Cauchy problem in the Gevre type multianisotropic spaces. Necessary and sufficient conditions for unique solvability of this problem are obtained and the properties of operators (polynomials) that are hyperbolic with a specified weight are investigated. PubDate: 2018-11-01 DOI: 10.3103/S1068362318060018
Abstract: In this paper, we study certain classes of analytic functions which satisfy a subordination condition and are associated with the crescent-shaped regions. We first give certain integral representations for the functions belonging to these classes and also present a relevant example. Making use of some known lemmas, we derive sufficient conditions for the functions to be in these classes. Some results on coefficient estimates are also obtained. PubDate: 2018-11-01 DOI: 10.3103/S1068362318060067
Abstract: In the present paper, estimates of the partial moduli of smoothness of fractional order of the conjugate functions of several variables are obtained in the space C(Tn). The accuracy of the obtained estimates is established by appropriate examples. PubDate: 2018-09-01 DOI: 10.3103/S1068362318050060
Abstract: In this paper, we prove that a set E is an M*-set or an AM*-set for the Franklin system if and only if E contains a nonempty perfect set. PubDate: 2018-09-01 DOI: 10.3103/S1068362318050047
Abstract: In this paper we study the maximal operator for a class of subsequences of strong Nörlund logarithmic means of Walsh-Fourier series. For such a class we prove the almost everywhere strong summability for every integrable function f. PubDate: 2018-09-01 DOI: 10.3103/S1068362318050059
Abstract: In this paper, for an one-dimensional semilinear wave equation we study a mixed problem with a nonlinear boundary condition. The questions of uniqueness and existence of global and blow-up solutions of this problem are investigated, depending on the nonlinearity nature appearing both in the equation and in the boundary condition. PubDate: 2018-09-01 DOI: 10.3103/S1068362318050011
Abstract: In this note, we study the admissible meromorphic solutions for algebraic differential equation fnf' + Pn−1(f) = R(z)eα(z), where Pn−1(f) is a differential polynomial in f of degree ≤ n − 1 with small function coefficients, R is a non-vanishing small function of f, and α is an entire function. We show that this equation does not possess any meromorphic solution f(z) satisfying N(r, f) = S(r, f) unless Pn−1(f) ≡ 0. Using this result, we generalize a well-known result by Hayman. PubDate: 2018-09-01 DOI: 10.3103/S1068362318050023
Abstract: In this paper, we derive characterizations of boundedness of subsequences of partial sums with respect to Vilenkin system on the martingale Hardy spaces Hp when 0 < p < 1. Moreover, we find necessary and sufficient conditions for the modulus of continuity of martingales f ∈ Hp, which provide convergence of subsequences of partial sums on the martingale Hardy spaces Hp. It is also proved that these results are the best possible in a special sense. As applications, some known and new results are pointed out. PubDate: 2018-09-01 DOI: 10.3103/S1068362318050072
Abstract: Suppose φ is a holomorphic self map of the unit disk and Cφ is a composition operator with symbol φ that fixes the origin and 0 < φ'(0) < 1. This paper explores sufficient conditions that ensure all the holomorphic solutions of Schröder equation for the composition operator Cφ to belong to a Bloch-type space Bα for some α > 0. In the second part of the paper, the results obtained for composition operators are extended to the case of weighted composition operators. PubDate: 2018-09-01 DOI: 10.3103/S1068362318050035
Abstract: In this paper, theorems about asymptotic behavior of the local probabilities of crossing the linear boundaries by a perturbed random walk are proved. PubDate: 2018-07-01 DOI: 10.3103/S1068362318040052
Abstract: The paper considers the general Franklin system corresponding to a regular by couples partition of the segment [0; 1]. For series by this system, we prove uniqueness theorems and obtain restoration formulas for coefficients, provided that the series converge in measure and satisfy some necessary condition. PubDate: 2018-07-01 DOI: 10.3103/S1068362318040040
Abstract: In this paper the unique solvability of regular hypoelliptic equations in multianisotropic weighted functional spaces is proved by means of special integral representation of functions through a regular operator. The existence of the solutions is proved by constructing approximate solutions using multianisotropic integral operators. PubDate: 2018-07-01 DOI: 10.3103/S1068362318040015
Abstract: We introduce two types of estimators of the finite–dimensional parameters in the case of observations of inhomogeneous Poisson processes. These are the estimators of the method of moments and Multi–step MLE. It is shown that the estimators of the method of moments are consistent and asymptotically normal and the Multi–step MLE are consistent and asymptotically efficient. The construction of Multi–step MLE–process is done in two steps. First we construct a consistent estimator by the observations on some learning interval and then this estimator is used for construction of One–step and Two–step MLEs. The main advantage of the proposed approach is its computational simplicity. PubDate: 2018-07-01 DOI: 10.3103/S1068362318040064
Abstract: A system of nonlinear integral equations with a convolution type operator arising in the p–adic string theory for the scalar tachyons field is studied. The existence of a one–parameter family of monotone continuous and bounded solutions for this system is proved. The limits of the constructed solutions at ±∞ are calculated. PubDate: 2018-07-01 DOI: 10.3103/S1068362318040027
Abstract: Some extensions of the results of the first author related with the Hilbert spaces A ω,0 2 of functions holomorphic in the half–plane are proved. Some new Hilbert spaces A ω 2 of Dirichlet type are introduced, which are included in the Hardy space H2 over the half–plane. Several results on representations, boundary properties, isometry, interpolation, biorthogonal systems and bases are obtained for the spaces A ω 2 ⊂ H2. PubDate: 2018-07-01 DOI: 10.3103/S1068362318040039
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