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1.
L. P. Il'ina 《Mathematical Notes》1968,4(6):918-922
In the class S of functionsf(z)=z+c2z2+c3z3+..., regular and univalent in ¦z¦<1, the following bound is obtained: cn+1¦–¦cn<4.26, n=1, 2, ...Translated from Matematicheskie Zametki, Vol. 4, No. 6, pp. 715–722, December, 1968.I wish to express my sincere thanks to I. M. Milin for a series of useful conversations. 相似文献
2.
Let A denote the class of functions which are analytic in |z|<1 and normalized so that f(0)=0 and f′(0)=1, and let R(α, β)⊂A
be the class of functions f such thatRe[f′(z)+αzf″(z)]>β,Re α>0, β<1. We determine conditions under which (i) f ∈ R(α1, β1), g ∈ R(α2, β2) implies that the convolution f×g of f and g is convex; (ii) f ∈ R(0, β1), g ∈ R(0, β2) implies that f×g is starlike; (iii) f≠A such that f′(z)[f(z)/z]μ-1 ≺ 1 + λz, μ>0, 0<λ<1, is starlike, and (iv) f≠A such that f′(z)+αzf″(z) ≺ 1 + λz, α>0, δ>0, is convex or starlike. Bibliography:
16 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 138–154. 相似文献
3.
E. G. Goluzina 《Journal of Mathematical Sciences》1996,79(5):1304-1307
We study the structural properties of the class Mk,λ,b(k≥2, 0≤λ≤1, b∈ℂ\{0}) of functions f(z)=z+ ... which are regular in |z|<1 and satisfy the conditions f(z)f′(z)z−1≠0 and
, where J(z)=λ(1+b−1zf″(z)/f′(z)+(1−λ)(b−1zf′(z)/f(z)+1−b−1). The value regions of some functionals on this class are found. The case λ=1 was considered in our previous paper. Bibliography:
4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 55–60.
Translated by O. A. Ivanov. 相似文献
4.
E. G. Goluzina 《Journal of Mathematical Sciences》1997,83(6):745-749
Let Mk,λ(0≤λ≤1, k≥2) be the class of functions f(z)=1/z+ao+a1z+... that are regular and locally univalent for 0<⩛z⩛<1 and satisfy the condition
where Jλ(z)=λ(1+zf″(z)/f'(z))+(1-λ)zf'(z)/f(z). In the class Mk,λ we consider sorne coefficient problems and problems concerning distortion theorems.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 212, 1994, pp. 91–96.
Translated by N. Yu. Netsvetaev. 相似文献
5.
E. G. Goluzina 《Journal of Mathematical Sciences》1998,89(1):958-966
Let TR be the class of functions
that are regular and typically real in the disk E={z:⋱z⋱<1}. For this class, the region of values of the system {f(z0), f(r)} for z0 ∈ ℝ, r∈(-1,1) is studied. The sets Dr={f(z0):f∈TR, f(r)=a} for −1≤r≤1 and Δr={(c2, c3): f ∈ TR, −f(−r)=a} for 0<r≤1 are found, where aε(r(1+r)−2, r(1−r)−2) is an arbitrary fixed number. Bibliography: 11 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 69–79. 相似文献
6.
For given analytic functions ϕ(z) = z + Σ
n=2∞ λ
n
z
n
, Ψ(z) = z + Σ
n=2∞ μ with λ
n
≥ 0, μ
n
≥ 0, and λ
n
≥ μ
n
and for α, β (0≤α<1, 0<β≤1), let E(φ,ψ; α, β) be of analytic functions ƒ(z) = z + Σ
n=2∞
a
n
z
n
in U such that f(z)*ψ(z)≠0 and
for z∈U; here, * denotes the Hadamard product. Let T be the class of functions ƒ(z) = z - Σ
n=2∞|a
n
| that are analytic and univalent in U, and let E
T
(φ,ψ;α,β)=E(φ,ψ;α,β)∩T. Coefficient estimates, extreme points, distortion properties, etc. are determined for the class E
T
(φ,ψ;α,β) in the case where the second coefficient is fixed. The results thus obtained, for particular choices of φ(z) and ψ(z), not only generalize various known results but also give rise to several new results.
University of Bahrain, Isa Town, Bahrain. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1162–1170,
September, 1997. 相似文献
7.
F. A. Shamoyan 《Journal of Mathematical Sciences》2006,139(2):6491-6495
Let ϕ(r) = (ϕ1(r1), …, ϕn(rn)) be a vector-valued function on R
+
n
. A necessary and sufficient condition is obtained under which any function f ∈, H∞ (D
n
), f(z) ≠ 0, z ∈, D
n
, is cyclic in the corresponding weighted space Lp(ϕ), where D
n
is the unit polydisk in C
n. Bibliography: 13 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 226–234. 相似文献
8.
Let L
p
(S), 0 < p < +∞, be a Lebesgue space of measurable functions on S with ordinary quasinorm ∥·∥
p
. For a system of sets {B
t
|t ∈ [0, +∞)
n
} and a given function ψ: [0, +∞)
n
↦ [ 0, +∞), we establish necessary and sufficient conditions for the existence of a function f ∈ L
p
(S) such that inf {∥f − g∥
p
p
g ∈ L
p
(S), g = 0 almost everywhere on S\B
t
} = ψ (t), t ∈ [0, +∞)
n
. As a consequence, we obtain a generalization and improvement of the Dzhrbashyan theorem on the inverse problem of approximation
by functions of the exponential type in L
2.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1116–1127, August, 2006. 相似文献
9.
V. A. Bykovskii 《Functional Analysis and Its Applications》2000,34(2):98-105
The Dirichlet (Hecke-Maass) series associated with the eigenfuctionsf andg of the invariant differential operator Δk=−y2(∂2/∂x2)+iky∂/∂x of weightk are investigated. It is proved that any relation of the form (f/kM)=g for thek-action of the groupSL
2
SL
2(ℝ) is equivalent to a pair of functional equations relating the Hecke-Maass series forf andg and involving only traditional gamma factors.
This work was supported by the Russian Foundation for Basic Research (grant No. 96-01-10439).
Institute of Applied Mathematics, Far East Division of Russian Academy of Sciences. Translated from Funktional'nyi Analiz
i Ego Prilozheniya, Vol. 34, No. 2, pp. 23–32, April–June, 2000.
Translated by V. M. Volosov 相似文献
10.
A. Yu. Solynin 《Journal of Mathematical Sciences》1996,79(5):1341-1358
We consider the class S1(τ), 0<τ<1, of functions f(z)=rz+a2z2+... that are regular and univalent in the unit disk U and have |f(z)|<1. We obtain sharp estimates for the 1-measure of the
sets {θ: |f(eiθ)|=1}. As a corollary, for the familiar class S we find Kolmogorov-type estimates for the sets {θ: |f(eiθ)|>M}, M>1, and prove inequalities for the harmonic measure, which are similar to those by Carleman-Milloux and Baernstein.
We also consider problems on distortion of fixed systems of boundary arcs in the classes of functions that are regular (or
meromorphic) and univalent in the disk or circular annulus. Bibliography: 23 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 115–142.
Translated by A. Yu. solynin. 相似文献
11.
G. A. Pereverzeva 《Ukrainian Mathematical Journal》1999,51(5):793-798
We estimate errors of projection methods for the solution of the Fredholm equaitons of the first kindAx=y+ζ with random perturbation ζ under the assumption that the integral operatorA has a (ϕ, β)-differentiable kernel and the mathematical expectation of ∥ξ∥2 does not exceed σ2. Under these assumptions, we obtain an estimate that is a complete analog of the well-known result by Vainikko and Plato
for the deterministic case where ∥ξ∥≤σ.
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51,
No. 5, pp. 713–717, May, 1999. 相似文献
12.
A. N. Dyogtev 《Algebra and Logic》1996,35(2):80-85
Let A⊆N={0,1,2,...} and β be an n-ary Boolean function. We call A a β-implicatively selector (β-IS) set if there exists an
n-ary selector general recursive function f such that (∀x1,...,xn)(β(χ(x1),...,χ(xn))=1⟹f(x1,...,xn)∈A), where χ is the characteristic function of A. Let F(m), m≥1, be the family of all d
m+1
*
-IS sets, where
, F(0)=N, and F(∞) is the class of all subsets in N. The basic result of the article says that the family of all β-IS sets coincides with one
of F(m), m≥0, or F(∞), and, moreover, the inclusions F(0)⊂F(1)⊂...⊂F(∞) hold.
Translated fromAlgebra i Logika, Vol. 35, No. 2, pp. 145–153, March–April, 1996. 相似文献
13.
We prove that, under certain conditions on a positive functionl continuous on [0, +∞], there exists an entire transcendental functionf of boundedl-index such that lnlnM
f(r)lnL(r),r→∞, whereM
f
(r)=max {|f(z)|: |z|=r} andL(r)=∫
0
r
l(t)dt. Ifl(r)=r
p-1
forr≥1, 0<ρ<∞, then there exists an entire functionf of boundedl-index such thatM
f
(r)≈r
p
.
Lvov University, Lvov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48, No. 9, pp. 1166–1182, September, 1996. 相似文献
14.
E. P. Golubeva 《Journal of Mathematical Sciences》2006,133(6):1611-1621
Let S2(q) be the set of primitive forms in the space S2(Γ0(q)) of holomorpic Γ0(q)-cusp forms of weight 2. Let f ∈ S2(q) and let Lf(S) be the L-function of f(z). It is proved that the set {log Lf(1), f ∈ S2(q)} has a limit distribution function. The rate of convergence to this limit function is estimated. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 15–32. 相似文献
15.
In the space of functions B
a3+={g(x, t)=−g(−x, t)=g(x+2π, t)=−g(x, t+T3/2)=g(x, −t)}, we establish that if the condition aT
3
(2s−1)=4πk, (4πk, a (2s−1))=1, k ∈ ℤ, s ∈ ℕ, is satisfied, then the linear problem u
u
−a
2
u
xx
=g(x, t), u(0, t)=u(π, t)=0, u(x, t+T
3
)=u(x, t), ℝ2, is always consistent. To prove this statement, we construct an exact solution in the form of an integral operator.
Ternopol’ Pedagogical Institute, Ternopol’. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 302–308,
Feburary, 1997
Ternopol’ Pedagogical Institute, Ternopol’. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 302–308,
Feburary, 1997 相似文献
16.
Let f(z) be a Hecke eigenform in the space S2k(Γ) of holomorphic Γ-cusp forms of even weight 2k, Γ=SL(2,ℤ); let Lf(s) be the L-function of f(z). The goal of this paper is to obtain some results on Lf(1) as k increases. In particular, we prove an analogue of the classical Landau theorem in the theory of Dirichlet L-functions
and (under a very plausible hypothesis) an analogue of the famous Siegel theorem. Bibliography: 15 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 37–54.
Translated by E. P. Golubeva. 相似文献
17.
In this paper we consider the intersection of the circle ¦w|=x with the image of the disc ¦z|≤r, 0f(z)=z+c2z2+... which is univalent analytic in ¦z|<1. Earlier I. E. Bazilevich proved that for xc/er the measure of the above intersection does not exceed the measure of the intersection produced by the functionf
*(z)=z/(1–z)2, ¦=1. In this paper I. E. Bazilevich's ideas are used to strengthen some of his results.Translated from Matematicheskie Zametki, Vol. 18, No. 3, pp. 367–378, September, 1975. 相似文献
18.
Assume thatf is an integer transcendental solution of the differential equationP
n
(z, f, f′)=P
n−1(z, f, f′, ... f
(p)), whereP
n
andP
n−1 are polynomials in all variables, the degree ofP
n
with respect tof andf′ is equal ton, and the degree ofP
n−1 with respect tof, f′, ... f
(p) is at mostn−1. We prove that the order ρ of growth off satisfies the relation 1/2≤ρ<∞. We also prove that if ρ=1/2, then, for a certain real ν, in the domain {z: ν<argz<ν+2π}/E
*, whereE
* is a certain set of disks with finite sum of radii, the estimate lnf(z)=z
1/2 (β+o(1)), β∈C, holds forz=re
iϕ,r≥r(ϕ)≥0. Furthermore, on the ray {z: argz=ν}, the following relation is true: ln‖f(re
iν)‖=o(r
1/2),r→+∞,r>0,
, where Δ is a certain set on the semiaxisr>0 with mes Δ<∞.
“L'vivs'ka Politekhnika” University, Lvov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 69–77,
January, 1999. 相似文献
19.
E. G. Goluzina 《Journal of Mathematical Sciences》2006,137(3):4774-4779
The paper studies the region of values Dm,1(T) of the system {ƒ(z1), ƒ(z2), …, ƒ(zm), ƒ(r)}, m e 1, where zj (j = 1, 2, …,m) are arbitrary fixed points of the disk U = {z: |z| < 1} with Im zj ≠ 0 (j = 1, 2, …,m), and r, 0 < r < 1, is fixed, in the class T of functions ƒ(z) = z+a2z2+ ⋯ regular in the disk U and satisfying in the latter the condition Im ƒ(z) Imz > 0 for Im z ≠ 0. An algebraic characterization of the set Dm,1(T) in terms of nonnegative-definite Hermitian forms is given, and all the boundary functions are described. As an implication,
the region of values of ƒ(zm) in the subclass of functions from the class T with prescribed values ƒ(zk) (k = 1, 2, …,m − 1) and ƒ(r) is determined. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 24–33. Original article submitted June 13, 2005. 相似文献
20.
D. Z. Arov 《Journal of Mathematical Sciences》1985,31(1):2645-2659
We consider the class II of operator functions f(z), meromorphic for ¦z¦1, which admit a representation in the form f(z)=f
2
–1
(z)f1(z), where f1(z) is an operatorvalued holomorphic function and f2(z) a scalar-valued bounded holomorphic function, such that the strong limits and coincide a.e. on the unit circle ¦¦=1. We prove that any function of class II can be represented as a block of some J-inner function of class II. We describe all such representations. The results found are applied to the question of realizations of functions of class II as transfer functions of linear systems.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta.im. V. A. Steklova AN SSSR, Vol. 135, pp. 5–30, 1984. 相似文献