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1.
Let U be a subharmonic function in C with a Riesz mass , distributed on the negative semiaxis without some neighborhood of zero, let and be its order and lower order, and let B(r, U) be the maximum of U(z) for ¦z¦=r. Estimates are obtained for the measure of sets of those values of r 0 for which certain inequalities hold. The following result is typical. LetE = {r:u(re
l)–cosB<(r,U) > 0}. If < < 1, ¦¦=., then the lower logarithmic density of the set E is at least 1 – /. If < > 1,¦¦ ., then the upper logarithmic density of the set E is at least 1 – /.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 31–38, 1988. 相似文献
2.
We show that for any simple piecewise Ljapunov contour there exists a power weight such that the essential norm |S
| in the spaceL
2(, ) does not depend on the angles of the contour and it is given by formula (2). All such weights are described. For the union =12 of two simple piecewise Lyapunov curves we prove that the essential norm |S
| inL
2() is minimal if both 1 and 2 are smooth in some neighborhoods of the common points. It is the case when the norm |S
| in the spaceL
2() as well as inL
2(, ) does not depend on the values of the angles and it can be calculated by formula (5). 相似文献
3.
(0; 0, 1) , {x
k
<x
k
*
<x
k+1}
k=1
n–1
{x
k
k=1
n
}., I, ,
n
(x)=P
n
(, )
(x)–n- , =, n3 . , x
0=+1 x
n+1= –1. II .
To the memory of Paul Erds
The research was supported by the Hungarian National Foundation for Scientific Research under Grant # T 914 244. 相似文献
To the memory of Paul Erds
The research was supported by the Hungarian National Foundation for Scientific Research under Grant # T 914 244. 相似文献
4.
D. V. Millionshchikov 《Mathematical Notes》2005,77(1-2):61-71
The cohomology H* (G/,) of the de Rham complex *(G/) of a compact solvmanifold G/ with deformed differential d = d + , where is a closed 1 -form, is studied. Such cohomologies naturally arise in Morse-Novikov theory. It is shown that, for any completely solvable Lie group G containing a cocompact lattice G, the cohomology H*(G/, ) is isomorphic to the cohomology H*(
) of the tangent Lie algebra
of the group G with coefficients in the one-dimensional representation :
defined by () = (). Moreover, the cohomology H
*(G/,) is nontrivial if and only if -[] belongs to a finite subset
of H
1(G/,) defined in terms of the Lie algebra
.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 67–79.Original Russian Text Copyright © 2005 by D. V. Millionshchikov.This revised version was published online in April 2005 with a corrected issue number. 相似文献
5.
Let G be a finite permutation group on a set with no fixed points in and let m and k be integers with 0 < m < k. For a finite subset of the movement of is defined as move() = maxgG| g \ |. Suppose further that G is not a 2-group and that p is the least odd prime dividing |G| and move() m for all k-element subsets of . Then either || k + m or k (7m – 5) / 2, || (9m – 3)/2. Moreover when || > k + m, then move() m for every subset of . 相似文献
6.
We consider a selfadjoint and smooth enough operator-valued functionL() on the segment [a, b]. LetL(a)0,L(b)0, and there exist two positive numbers and such that the inequality |(L()f, f)|< ([a, b] f=1) implies the inequality (L'()f, f)>. Then the functionL() admits a factorizationL()=M()(I-Z) whereM() is a continuous and invertible on [a, b] operator-valued function, and operatorZ is similar to a selfadjoint one. This result was obtained in the first part of the present paper [10] under a stronge conditionL()0 ( [a,b]). For analytic functionL() the result of this paper was obtained in [13]. 相似文献
7.
Mark Skandera 《Journal of Algebraic Combinatorics》2004,20(2):195-211
Let
I,I be the minor of a matrix which corresponds to row set I and column set I. We give a characterization of the inequalities of the form
I,I
K,K
J,J
L,L
which hold for all totally nonnegative matrices. This generalizes a recent result of Fallat, Gekhtman, and Johnson. 相似文献
8.
Let
n
be n-dimensional Euclidean space, and let : [0, L]
n
and : [0, L]
n
be closed rectifiable arcs in
n
of the same total length L which are parametrized via their arc length. is said to be a chord-stretched version of if for each 0s tL, |(t)–(s)| |(t)–(s)|. is said to be convex if is simple and if ([0, L]) is the frontier of some plane convex set. Individual work by Professors G. Choquet and G. T. Sallee demonstrated that if were simple then there existed a convex chord-stretched version of . This result led Professor Yang Lu to conjecture that if were convex and were a chord-stretched version of then and would be congruent, i.e. any chord-stretching map of a convex arc is an isometry. Professor Yang Lu has proved this conjecture in the case where and are C
2 curves. In this paper we prove the conjecture in general. 相似文献
9.
10.
Erik Valtonen 《manuscripta mathematica》1989,63(1):45-68
LetR be a commutative ring with 1 andM anR-module. If:M
R
MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR
M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR
M; in particular, we are interested in some homological properties ofR
M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR
M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM
*, where the isomorphism is given by the adjoint of. 相似文献
11.
J. Lippus 《Analysis Mathematica》1984,10(3):213-231
- ()N2,L
F
(
) — , 2- , {s
m()
f} -L.
— . (L
F(
),L
F(
) ={(k)} (kZ2) , fLF(
) f
,
, L
F(
). - ={()} ={()} , n(())m()n(()+())
. R() , ..
- . , . (L
F
(
),L
F
(
)) , R(,)=O(1) (x).
The author wishes to express his gratitude to S. A.Teljakovski for setting the problem and for his attention to this paper. 相似文献
The author wishes to express his gratitude to S. A.Teljakovski for setting the problem and for his attention to this paper. 相似文献
12.
A. N. Bakhvalov 《Analysis Mathematica》2001,27(1):3-36
Let a ={nlna (n+1)}, where a R. The following results are established: For every &fnof a BV ((- ]2), the triangular partial sums of its Fourier series are uniformly bounded if a = -1, and converge everywhere if a < -1.For every a>0, there exists &fnof a BV ((- ]2) such that the triangular partial sums of its Fourier series are unbounded at the point (0;0). 相似文献
13.
A. Yu. Šadrin 《Analysis Mathematica》1986,12(3):175-184
. L
p
, 0<p<, . , f, {E
n
(f)
p
}
1
p>0 .
The author expresses his thanks to S. B. Stekin for the attention he has paid to this work. 相似文献
The author expresses his thanks to S. B. Stekin for the attention he has paid to this work. 相似文献
14.
Certain Convolution Operators for Meromorphic Functions 总被引:3,自引:0,他引:3
Dinggong Yang 《Southeast Asian Bulletin of Mathematics》2001,25(1):175-186
Let (p N) be the class of functions
analytic in 0 < |z| < 1. A convolution operator Lp(a, c) on p is introduced. This paper gives some sharp inequalities for f(z) satisfying Re{(1 – )zpLp(a, c) f(z) + zpLp(a + 1, c) f(z)} > , where 0, < 1, a > 0 and c 0, –1, –2,....AMS Subject Classification (1991) 30C45 30A10 相似文献
15.
16.
K. Tandori 《Analysis Mathematica》1980,6(2):157-164
. . . : sn(x) — , n-(, 1)- n
L
2. , . , :
a
k
l
2
n
() [0,1] , (*) , (**) .
a
k
l
2
u
n
() [0,1] , (**), (*) . 相似文献
17.
Nous donnons une caractérisation des domaines DX pour lesquels la fonction extrémale relative *(,E,D) a la propriété de stabilité pour tout ED, i.e. lim
k*(,E,D
k
)=*(,E,D), ED. Ensuite, nous étudions la relation entre cette propriété et les enveloppes pluripolaires. Nous concluons par quelques remarques sur la propriété de stabilité lim
k*(,E
k
,D)=*(,E,D). 相似文献
18.
Let w be an element of the Weyl group of sl
n + 1. We prove that for a certain class of elements w (which includes the longest element w0 of the Weyl group), there exist a lattice polytope R
l(w)
, for each fundamental weight i of sl
n + 1, such that for any dominant weight =
i = 1
n
a
i
i
, the number of lattice points in the Minkowski sum
w
=
i = 1
n
a
i
i
w
is equal to the dimension of the Demazure module E
w
(). We also define a linear map A
w
: R
l(w)
P Z R where P denotes the weight lattice, such that char E
w
() = e
e–A(x)
where the sum runs through the lattice points x of
w
. 相似文献
19.
B. T. Rumov 《Mathematical Notes》1976,19(4):376-382
This paper proves the existence of resolvable block designs with divisibility into groups GD(v; k, m; 1, 2) without repeated blocks and with arbitrary parameters such that 1 = k, (v–1)/(k–1) 2 vk–2 (and also 1 k/2, (v–1)/(2(k–1)) 2 vk–2 in case k is even) k 4 andp=1 (mod k–1), k < p for each prime divisor p of number v. As a corollary, the existence of a resolvable BIB-design (v, k, ) without repeated blocks is deduced with X = k (and also with = k/2 in case of even k) k
, where a is a natural number if k is a prime power and=1 if k is a composite number.Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 623–634, April, 1976. 相似文献
20.
Roland Wolff 《Integral Equations and Operator Theory》2000,38(1):120-127
In this paper, we prove that the Hardy spaceH
p
(), 1p<, over a strictly pseudoconvex domain in
n
with smooth boundary is quasi-coherent. More precisely, we show that Toeplitz tuplesT
with suitable symbols onH
p
() have property (). This proof is based on a well known exactness result for the tangential Cauchy-Riemann complex. 相似文献