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1.
S. V. Kislyakov 《Journal of Mathematical Sciences》1997,85(2):1808-1813
Assume that 0<ε≤1, F ∈ C(
), E={≠0}, δ>0. Then there exists a function G with uniformly convergent Fourier series such that |G|+|F−G|≤(1+δ)|F|, m{F≠G}≤εmE,
and
. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 83–91. 相似文献
2.
K. M. D'yakonov 《Journal of Mathematical Sciences》1996,78(2):131-141
Let ϕ be a unimodular function on the unit circle
and let Kp(ϕ) denote the kernel of the Toeplitz operator Tϕ in the Hardy space Hp, p≥1;
. Suppose Kp(ϕ)≠{0}. The problem is to find out how the smoothness of the symbol ϕ influences the boundary smoothness of functions in
Kp(ϕ). One of the main results is as follows.
Theorem 1 Let 1<p, q<+∞, 1<r≤+∞, q−1=p−1+r−1. Suppose |ϕ|≡1 on
and ϕ∈W
r
1
(i.e.,
). Then Kp(ϕ)⊂W
q
1
. Moreover, for any f∈Kp(ϕ) we have ‖f′‖q≤c(p, r)‖ϕ′‖r ‖f‖. Bibliography: 19 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 201, 1992, pp. 5–21.
Translated by K. M. D'yakonov. 相似文献
3.
4.
A. B. Aleksandrov 《Journal of Mathematical Sciences》2000,101(3):3049-3052
We present an example of a set {
} satisfying the following two conditions: (1) there exists a nonzero positive singular measure on the unit circle {
} with spectrum in Λ; (2) if the spectrum of f∈L1 {
} is contained in Λ and f vanishes on a set of positive measure, then f=0. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 7–14.
Translated by A. B. Aleksandrov. 相似文献
5.
Let F be a subfield of a commutative field extending ℝ. Let
We say thatf :
preserves distanced ≥ 0 if for eachx,y ∈ ℝ ∣x- y∣= d implies ϕ2(f(x),f(y)) = d2
. We prove that each unit-distance preserving mappingf :
has a formI o (ρ,ρ), where
is a field homomorphism and
is an affine mapping with orthogonal linear part. 相似文献
6.
A. B. Aleksandrov 《Journal of Mathematical Sciences》1998,92(1):3550-3559
The main goal of this paper is to prove the following statement. Let
be a function holomorphic and of bounded characteristic in the unit disk
, where E is a Λ(1)-subset of ℤ+. Assume that f has a pseudocontinuation of bounded characteristic to the annulus {zɛℂ:1<|z|<R}. Then f admits analytic continuation
to the disk R
. In particular, f is a polynomial if R=+∞. Bibliography: 16 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 16–32.
Translated by A. B. Aleksandrov. 相似文献
7.
K. I. Beidar M. Bre@scaron;ar M. A. Chebotar 《Journal of Mathematical Sciences》2000,102(6):4557-4565
Let
, be the algebra of upper triangular r×r matrices over field aF. We describe multilinear maps
, where n≤r, such that [f(A,...,A), A]=0 for all
, provided that |F| >n + 1. As an application of the results obtained, we describe linear automorphisms θ of
such that [θ(A2), θ(A)]=0 for all
.
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 74, Algebra-15,
2000. 相似文献
8.
A. B. Aleksandrov 《Journal of Mathematical Sciences》1998,92(1):3543-3549
Let θ be an inner function. The main aim of this paper is to describe all positive measures on the unit circle
such that
for all continuous functions f∈H2⊖θH2. Bibliography: 8 titles.
Translated fromZapiski Nauchnykh Serninarov POMI, Vol. 232, 1996, pp. 5‐15.
Translated by V. V. Kapustin. 相似文献
9.
M. B. Zvyagina 《Journal of Mathematical Sciences》1998,89(2):1122-1126
Let Λ be an associative ring with identity and let
be the category of left unitary Λ-modules. A subcateqory
of the category
is said to be small if the pairwise nonisomorphic objects of
form a set. The main result of this paper consists of the fact that for every small full subcategory
, there exists a ring Γ such that
is dual to a small full subcategory of the category
. Some applications of this result are indicated. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 66–73. 相似文献
10.
For the problemP(λ): Maximizec
T
z subject toz∈Z(λ), whereZ(λ) is defined by an in general infinite set of linear inequalities, it is shown that the value-function has directional derivatives
at every point
such thatP(
) and its dual are both superconsistent. To compute these directional derivatives a min-max-formula, well-known in convex
programming, is derived. In addition, it is shown that derivatives can be obtained more easily by a limit-process using only
convergent selections of solutions ofP(λ
n
), λ
n
→
and their duals. 相似文献
11.
A. V. Demyanov 《Journal of Mathematical Sciences》2006,136(2):3706-3717
The problem of establishing necessary and sufficient conditions for l.s.c. under PDE constraints is studied for a special
class of functionals:
with respect to the convergence un → u in measure, vn ⇀ v in Lp(Ω;ℝd)
in W−1,p(Ω), and χn ⇀ χ in Lp(Ω), where χn ∈ Z:= {χ ∈ L∞(Ω): 0 ≤ χ(x) ≤ 1 for a.e. x}. Here
is a constant-rank partial differential operator. The main result is that if the characteristic cone of
has the full dimension, then the l.s.c. is equivalent to the fact that the F± are both
-quasiconvex and
for a.e. x ∈ Ω and for all u ∈ ℝd. As a corollary, we obtain several results for the functional
with respect to the same convergence. We show that this functional is l.s.c. iff
Bibliography: 14 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 100–119. 相似文献
12.
V. L. Oleînik 《Journal of Mathematical Sciences》2000,101(3):3133-3138
Let {
}, where {
} is the open unit disk on the complex plane {
}. In G, we consider analytic solutions u(t, z) ({
}, {
}) of the heat equation 2ut=uzz with initial data f(z)=u(0, z) belonging to the Fock space F, i.e., to the space of entire functions square summable with
the weight e−|z|2.Conditions on a nonnegative measure μ on G are described under which for all f ∈ F we have {
} Bibliography: 17 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 146–155.
Translated by S. V. Kislyakov. 相似文献
13.
A. O. Gokhman 《Journal of Mathematical Sciences》2000,101(3):3073-3087
This article is devoted to the study of representations of Ck {
} functions f invariant with respect to finite Coxeter groups W in the form f=F op, where p is a base in the algebra of W-invariant
polynomials. We examine the lowering of smoothness of F as compared with f and conclude that this lowering has an anisotropic
nature and that, more precisely, at each point Po it is described by a vector {
}. We examine the cases W=An, Bn, Dn, {
}; in each case the greatest component {
} of {
} is equal to the Coxeter number of the stabilizer Wyo of the point yo, where po=p(yo). Bibliography: 22 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 46–70.
Translated by S. Yu. Pilyugin. 相似文献
14.
Ludvik Janos 《Annali di Matematica Pura ed Applicata》1977,112(1):273-283
Summary We consider the boundary value problem αz″(x)+m(x)y(x)=0, αy″(x)+p(x)z(x)=0, xε[0, 1], y(0)=y(1)=z(0)=0, where the functions m(x) and p(x) are assumed integrable and positive everywhere in [0, 1]. As the main result we obtain the inequalities
for n=1, 2, ... where δn(m, p) stands for the product
of the first n eigenvalues αi(m, p) of the above system and where δn(m) abbreviates δn(m, m).
Entrata in Redazione il 6 febbraio 1976. 相似文献
15.
16.
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
17.
B. N. Khabibullin 《Mathematical Notes》1999,66(4):495-506
Letf be an entire function in
. For a broad class of distribution densities of the set Λ, a scale of sufficient conditions for the completeness of the system
of functions {f(λ×z):λ∈Λ},z∈E, where
, in the spaceH(E) of holomorphic functions onE with respect to the topology of uniform convergence on compact subsets is given in terms of the mutual indicator of the functionf and the setE. These conditions are new already forn=1 even ifE is a disk.
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 603–616, October, 1999. 相似文献
18.
T. I. Seidman S. A. Avdonin S. A. Ivanov 《Journal of Fourier Analysis and Applications》2000,6(3):233-254
Under a suitable sparsity condition on the exponents Λ=(λk=τk+iσk), it is shown that the individual terms
can be obtained from observation of the L2 function
through the ‘window’ t∈[0, δ]—with an l2 estimate (uniform for such Λ) asymptotically as t, δ→0. Some applications are given to control theory for partial differential
equations. 相似文献
19.
An estimate of
, Ω′⊃⊃Ω, for solutions uε of the family of equations
with a nondifferentiable lower term a is given. The majorant in the estimate depends on
and the distance between Ω′ and ∂Ω, and does not depend on ε. This publication is related to [2, 3]. Bibliography: 4 titles.
Dedicated to V. A. Solonnikov on his sixtieth anniversary
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 213, 1994, pp. 75–92.
Translated by O. A. Ladyzhenskaya and N. N. Uraltseva. 相似文献
20.
A. N. Degtev 《Mathematical Notes》1999,66(2):148-152
LetA be a subset of
, and leta∉A. The setA is said to be almost semirecursive, if there is a two-place general recursive functionf such thatf(x, y)ε{x, y, a}∧({x, y}⊆A⇌f(x, y)εA) for all
. Among other facts, it is proved that ifA and
are almost semirecursive sets, thenA is a semirecursive set, and that there exists a wsr*-set that is neither a wsr-nor an almost semirecursive set.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 188–193, August, 1999. 相似文献