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1.
A. G. Babenko 《Mathematical Notes》1996,60(3):248-263
In this paper we prove the Jackson-Stechkin inequalityE
n−1(f)<ω
n
(f, 2τ
n
,λ),n≥1,m≥5,r≥1, f ∈L2(
),f ≢ const, which is sharp for eachn=2, 3, ...; hereE
n−1
(f) is the best approximation of a functionf by spherical polynomials of degree ≤n−1, ω
n
(f, τ) is theτth modulus of continuity off based on the translations
,t ∈ ℝ,x ∈
,
,
is the measure of the unit Euclidean sphere
,
, andτ
n
,λ is the first positive zero of the Gegenbauer cosine polynomial
(cost).
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 333–355, September, 1996.
The present paper was discussed at Ural State University in a seminar headed by Professor Arestov. The author is grateful
to Professor Arestov and Associate Professor Popov for useful conversations.
This research was supported by the State Commission for Higher Education of the Russian Federation under grant No. 2-16-5-31
and by the Russian Foundation for Basic Research under grant No. 93-011-196. 相似文献
2.
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
3.
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
4.
In this paper we consider special elements of the Fock space #x2131;
n
. That is the space of entire functionsf:ℂ:
n
→ℂ, such that the followingL
2- condition is satisfied:
. Here we show that there exists an entire functiong:ℂ
n
→ℂ such that for every one-dimensional subspace Π⊂ℂ
n
and for all 0<∈<2 we have
, but in the limit case ∈=0 we have
. This result is analogue to a result from [1]. There holomorphic functions on the unit-ball are investigated. Furthermore
the proof — as the one in [1] — uses a theorem from [2]. Therefore we give another application of the results from [2] — namely
for spaces of entire functions. 相似文献
5.
Kai WANG 《数学年刊B辑(英文版)》2007,28(3):321-326
Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd). 相似文献
6.
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
7.
Piotr Kot 《Czechoslovak Mathematical Journal》2007,57(1):29-47
We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball
For a function u which is lower semi-continuous on
we give necessary and sufficient conditions in order that there exists a holomorphic function f ∈
such that
. 相似文献
8.
In the paper we study a binding boundary value problem for two media for Poisson's equation μΔu=f(x) with solutions in the class
, 1<p<∞, with the corresponding seminorm, where
It is proved that the solution exists for allf(x)∈L
p
, anda priori estimates of the solution are obtained with the help of multiplicators in the space
. An explicit solution of the problem for all
is obtained. The kernel of the operator generated by the problem is constructed (in explicit form) as a polynomial of the
first degree.
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 515–526, October, 1999. 相似文献
9.
We give the “boundary version” of the Boggess-PolkingCR extension theorem. LetM andN be real generic submanifolds of ℂ
n
withN ⊂M and letV be a “wedge” inM with “edge”N and “profile” Σ ⊂T
NM in a neighborhood of a pointz
o.We identify in natural manner
and assume that for a holomorphic vector fieldL tangent toM and verifying
we have that the Levi form
takes a value
. Then we prove thatCR functions onV extend ∀ω to a wedgeV
1 “attached” toV in direction of a vector fieldiV such that |pr(iV(z
0))−iv
0| < ε (where pr is the projection pr:T
NX →T
MX |
N
).We then prove that when the Levi cone “relative to Σ”iZ
Σ = convex hull
is open inT
MX, thenCR functions extend to a “full” wedge with edgeN (that is, with a profile which is an open cone ofT
NX). Finally, we prove that iff is defined in a couple of wedges ±V with profiles ±Σ such thatiZ
Σ =T
MX, and is continuous up toN, thenf is in fact holomorphic atz
o. 相似文献
10.
11.
12.
S. Norvidas 《Lithuanian Mathematical Journal》2009,49(2):185-189
For a compact set K in ℝ
n
, let B
2
K
be the set of all functions f ∈ L
2(ℝ2) bandlimited to K, i.e., such that the Fourier transform f̂ of f is supported by K. We investigate the question of approximation of f ∈ B
2
K
by finite exponential sums
in the space , as τ → ∞. 相似文献
13.
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
14.
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
15.
Thomas Bartsch Zhi-Qiang Wang Juncheng Wei 《Journal of Fixed Point Theory and Applications》2007,2(2):353-367
We consider the existence of bound states for the coupled elliptic system
where n ≤ 3. Using the fixed point index in cones we prove the existence of a five-dimensional continuum of solutions (λ1, λ2, μ
1, μ
2, β, u
1, u
2) bifurcating from the set of semipositive solutions (where u
1 = 0 or u
2 = 0) and investigate the parameter range covered by .
Dedicated to Albrecht Dold and Edward Fadell 相似文献
16.
Piotr Kot 《Czechoslovak Mathematical Journal》2009,59(2):371-379
We solve the following Dirichlet problem on the bounded balanced domain with some additional properties: For p > 0 and a positive lower semi-continuous function u on ∂Ω with u(z) = u(λ z) for |λ| = 1, z ∈ ∂Ω we construct a holomorphic function f ∈ (Ω) such that for z ∈ ∂Ω, where = {λ ∈ ℂ: |λ| < 1}.
相似文献
17.
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
18.
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
19.
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
20.
For a nonempty setE of nonnegative integers letH
E
p, q, a
andH
E
p
be the closed linear span of
相似文献
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