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Том 217, № 1 (2016)
- Год: 2016
- Статей: 13
- URL: https://bakhtiniada.ru/1072-3374/issue/view/14758
Article
1-2
A Nonperiodic Spline Analog of the Akhiezer–Krein–Favard Operators
Аннотация
Let σ > 0, m, r ∈ ℕ, m ≥ r, let Sσ,m be the space of splines of order m and minimal defect with nodes \( \frac{j\pi }{\sigma } \) (j ∈ ℤ), and let Aσ,m(f)p be the best approximation of a function f by the set Sσ,m in the space Lp(ℝ). It is known that for p = 1,+∞,
3-22
Configuration Module and Removable Sets
Аннотация
In the paper, a new class of polycondensers, for which the capacity of a polycondenser equals its module, is introduced. It is established that the sets that are removable for the condenser’s capacity are also removable for the module of the polycondensers considered. Bibliography: 5 titles.
23-27
Distortion Theorems for Circumferentially Mean P -Valent Functions
Аннотация
Some distortion theorems for circumferentially mean p-valent functions are proved using the symmetrization method. The cases of functions with a zero of order p at the origin, functions having no zeros, and functions with Montel’s normalization are considered. The equality cases in the estimates obtained are described. Bibliography: 10 titles.
28-36
37-44
45-53
Two-Dimensional Approximations by the Method of Dividing Toric Tilings
Аннотация
An infinite sequence of dividing two-dimensional toric tilings is constructed by the differentiation method. The karyons of the tilings have radii tending to zero and contain points having the best approximations on the torus in certain normalized metrics, which are defined by the initial karyon. The properties of the latter metrics can be essentially different from those of the standard metrics on a torus, used in approximation problems.
54-64
65-80
Estimating the Norm of the Holomorphic Component of a Meromorphic Function in a Finitely Connected Domain
Аннотация
In this paper, we extend a Gonchar–Grigorjan type estimate for the norm of the holomorphic parts of meromorphic functions in finitely connected Jordan domains with C2-smooth boundary in the case where the poles are in a compact set. A uniform estimate for Cauchy type integrals is also given.
81-90
Normalized Incomplete Beta Function: Log-Concavity in Parameters and Other Properties
Аннотация
The logarithmic concavity/convexity in parameters of the normalized incomplete beta function has been established by Finner and Roters in 1997 as a corollary of a rather difficult result, based on generalized reproductive property of certain distributions. In the first part of this paper, a direct analytic proof of the logarithmic concavity/convexity mentioned above is presented. These results are strengthened in the second part, where it is proved that the power series coefficients of the generalized Turán determinants formed by the parameter shifts of the normalized incomplete beta function have constant sign under some additional restrictions. The method of proof suggested also leads to various other new facts, which may be of independent interest. In particular, linearization formulas and two-sided bounds for the above-mentioned Turán determinants, and also two identities of combinatorial type, which we believe to be new, are established.
91-107
Polarization and Circular Truncation of a Domain
Аннотация
The paper considers the difference between the reduced module m(D) of a simply connected domain D with respect to the point z = 0 and the reduced module m(Dr) of its radial circular truncation, where Dr is the connected component of the set D ∩ {|z| < r} containing the point z = 0. It is proved that this difference does not decrease under polarization and circular symmetrization.
108-113
114-124
On the Mean Square of the Error Term For Dedekind Zeta Functions
Аннотация
Let Kn be a number field of degree n over ℚ. By D(x,Kn) denote the number of all nonzero integral ideals in Kn with norm ≤ x. The Dedekind zeta function ζKn(s) is a meromorphic function with a simple pole at s = 1 and with residue, say, Λn. Define
125-137