共查询到20条相似文献,搜索用时 31 毫秒
1.
The paper is concerned with the sharpness of some well-known estimates in universal linear-invariant families
of regular functions. It is shown that the estimate of | arg ƒ′(z)|,z ∈ Δ = {z: |z| < 1} obtained by Pommerenke in 1964 is sharp; the extremal function is found. A lower estimate for the Schwarzian derivative
in
is obtained. For
, a sharp estimate of order of the function ƒr(z)=ƒ(rz)/r withr ∈ (0, 1) is found; this estimate is applied to solve other problems.
Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 665–672, May, 1998. 相似文献
2.
M. B. Khripunova 《Mathematical Notes》1998,64(3):394-400
It is proved that if ƒ(n) is a multiplicative function taking a valueζ on the set of primes such thatζ
3 = 1,ζ ≠ 1 andƒ
3(p
r)=1 forr≥2, then there exists aθ ∈ (0, 1), for which
, where
.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 457–464, September, 1998.
The author wishes to thank Professor N. M. Timofeev for useful discussions.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00502. 相似文献
3.
O. B. Skaskiv 《Mathematical Notes》1999,66(2):223-232
For an entire Dirichlet series
, sufficient conditions on the exponents
are established such that the following relations hold outside a set of finite measure asx→+∞:
, where ψ(x) is a function increasing to +∞ and such thatx≤ψ(x)≤e
x
(x≥0).
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 282–292, August, 1999 相似文献
4.
L. V. Kritskov 《Mathematical Notes》1999,65(4):454-461
Suppose thatА is a nonnegative self-adjoint extension to {
} of the formal differential operator−Δu+q(x)u with potentialq(x) satisfying the condition {
} or the condition {
} in which the nonnegative function itχ(r) is such that {
}. For each α∈(0, 2], we establish an estimate of the generalized Fourier transforms of an arbitrary function {
} of the form {
} If, in addition, {
}, then, along with this estimate, a similar lower bound is established.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 542–551, April, 1999. 相似文献
5.
A. V. Filinovskii 《Mathematical Notes》1997,61(5):635-643
The following boundary value problem is studied:
here the surface Г satisfies the condition(
, where
and ν is the outward (with respect to Ω) normal to Γ.
Translated fromMatematischskie Zametki, Vol. 61, No. 5, pp. 759–768, May, 1997.
Translated by N. K. Kulman 相似文献
6.
I. I. Sharapudinov 《Mathematical Notes》1997,62(4):501-512
Suppose that 0<δ≤1,N=1/δ, and α, ga≥0, is an integer. For the classical Meixner polynomials
orthonormal on the gird {0, δ, 2δ, ...} with weight ρ(x)=(1-e
−δ)αг(Nx+α+ 1)/г(Nx+1), the following asymptotic formula is obtained:
. The remainderv
n,N
α
(z) forn≤λN satisfies the estimate
where Λ
k
α
(x) are the Laguerre orthonormal polynomials. As a consequence, a weighted estimate, for the Meixner polynomial
on the semiaxis [0, ∞) is obtained.
Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 603–616, October, 1997.
Translated by N. K. Kulman 相似文献
7.
Consider the nonparametric regression model
, whereg is an unknown function to be estimated on [0, 1],
are the fixed design points in the interval [0, 1] and
is a triangular array of row iid random variables having median zero. The nearest neighbor median estimator
is taken as the estimator of the unknown functiong(x). Median cross validation (mev) criterion is employed to select the smoothing parameterh. Leth
π
*
be the smoothing parameter chosen by mev criterion. Under mild regularity conditions, the upper and lower bounds ofh
π
*
, the rate of convergence and the weak consistency of the median cross-validated estimate
are obtained.
Project supported by the National Natural Science Foundation of China and the Doctoral Foundation of Education of China. 相似文献
8.
L. I. Danilov 《Mathematical Notes》1997,61(1):48-57
We consider Stepanov almost periodic functions μ ∈
ranging in the metric space
of Borel probability measures on a complete separable metric space
is equipped with the Prokhorov metric). The main result is as follows: a function
, belongs to
if and only if for each bounded continuous function
, the function
is Stepanov almost periodic (of order 1) and
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 57–68, January, 1997.
Translated by I. P. Zvyagin 相似文献
9.
A. Ya. Khelemskii 《Mathematical Notes》1977,21(1):51-54
Let
and
be algebras of local and quasilocal observable spin systems corresponding to the group Zr,
be a differentiation invariant with respect to displacements. The question of representation of D in the form of formal Hamiltonian
formed by the displacements of an elementx ε
is considered. It is shown that such a representation exists if the condition
holds, where
means an element obtained from the elements [TkX,a] by some r-multiple process of summation.
Translated from Matematicheskii Zametki, Vol. 21, No. 1, pp. 93–98, January, 1977. 相似文献
10.
O. P. Filatov 《Mathematical Notes》1999,66(3):348-354
For a continuous almost periodic function
, we show that the function
where the supremum is taken over all solutions of the system of differential inclusion
,
, has the following limit (as μ→+0):
, Thus if the parameter μ is small, then
and the limit of the maximal mean can approximately be determined by solving problems of smaller dimensionality. Moreover,
if the compact sets
and
are nondegenerate, then Ψ
f
is independent of initial data.
Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 431–438, September, 1999. 相似文献
11.
A. A. Ryabinin 《Mathematical Notes》1998,64(5):629-633
The system
, where Λ={λ
n
} is the set of zeros (of multiplicitiesm
n
) of the Fourier transform
of a singular Cantor-Lebesgue measure, is examined. We prove thate(Λ) is complete and minimal inL
p
(−a, a) withp≥1, and that |L(x+iy)|2 does not satisfy the Muckenhoupt condition on any horizontal line Imz=y≠0 in the complex plane. This implies thate(Λ) does not have the property of convergence extension.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 728–733, November, 1998. 相似文献
12.
I. N. Brui 《Mathematical Notes》1997,62(5):566-574
Suppose that a lower triangular matrix μ:[μ
m
(n)
] defines a conservative summation method for series, i.e.,
and the sequence (ρ
m
,m ∈ ℤ0), is bounded away from zero. Then the trigonometric series
is the Fourier series of a functionf ∈L
p
(
), wherep ε ]1; ∞[, if and only if the sequence ofp-norms of its μ-means is bounded:
In the case of the Fejér method, we have the test due to W. and G. Young (1913). In the case of the Fourier method, we obtain
the converse of the Riesz theorem (1927).
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 677–686, November, 1997.
Translated by N. K. Kulman 相似文献
13.
Let μ be a positive Borel measure having support supp μ ⊂ [1, ∞) and satisfying the conditionf(t−1)−1dμ(t)<∞. In this paper we study the order of the uniform approximation of the function
on the disk |z|≤1 and on the closed interval [−1, 1] by means of the orthogonal projection of
on the set of rational functions of degreen. Moreover, the poles of the rational functions are chosen depending on the measure μ. For example, it is shown that if supp
μ is compact and does not contain 1, then this approximation method is of best order. But if supp μ=[1,a],a>1, the measure μ is absolutely continuous with respect to the Lebesgue measure, and
fort∈[1,a] and some α>0, then the order of such an approximation differs from the best only by
.
Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 362–368, March, 1999. 相似文献
14.
This paper deals with the problem of small oscillations in a liquid layer of finite depth under the assumption that the bottom
is an elastic medium. The system of equations corresponding to the problem is written out and explained. The main aim of the
paper is to recast these equations in the form
, where
and
are positive operators in the function space naturally corresponding to the problem. The further aim is to investigate the
spectrum of the linear pencil
, which determines the dynamics of the problem.
Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 66–81, July, 2000. 相似文献
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15.
A. V. Glushak 《Mathematical Notes》1996,60(3):269-273
The stability of the uniform correctness of the Cauchy problem
,t>0,u(0)=u
0,u′(0)=0 fork>0 with respect to perturbations of the operator
is studied.
Translated fromMatematickeskie Zameiki, Vol. 60, No. 3, pp. 363–369, September, 1996. 相似文献
16.
M. I. Anokhin 《Mathematical Notes》1997,61(1):3-8
LetF be a free group with at most countable system
of free generators, letR be its normal subgroup recursively enumerable with respect to
, and let
be a variety of groups that differs from
and for which the corresponding verbal subgroupV of the free group of countable rank is recursive. It is proved that the word problem inF/V(R) is solvable if and only if this problem is solvable inF/R, and if
, then there exists anR such, that the conjugacy problem inF/R is solvable, but this problem is unsolvable inF/V(R) for any Abelian variety
(all algorithmic problems are regarded with respect to the images of
under the corresponding natural epimorphisms).
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 3–9, January, 1997.
Translated by M. I. Anokhin 相似文献
17.
L. G. Arabadzhyan 《Mathematical Notes》1997,62(3):271-277
We study the solvability of the integral equation
, wheref∈L
1
loc(ℝ) is the unknown function andg,T
1, andT
2 are given functions satisfying the conditions
.
Most attention is paid to the nontrivial solvability of the homogeneous equation
.
Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 323–331, September, 1997.
Translated by M. A. Shishkova 相似文献
18.
Suppose that k and l are integers such that
and
, M
k is a set of numbers without kth powers, and
. In this paper, we obtain asymptotic estimates of the sums
over
相似文献
19.
V. Yu. Popov 《Mathematical Notes》2000,67(4):495-504
An example of a series of varieties of rings
with the finite basis property is constructed for which the word problem in the relatively free ring
of rankn in the variety
is decidable if and only ifn <p.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 582–594, April, 2000. 相似文献
20.