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1.
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
2.
Deh-phone Kung Hsing 《Annali di Matematica Pura ed Applicata》1976,109(1):235-245
Summary We consider the system(L):
, t ⩾ p, y(t)=f(t), t⩽0, where y is an n-vector and each Ai, B(t) are n × n matrices. System(L) generates a semigroup by means of Ttf(s)=y (t+s, f), f(s) ∈ BCl(− ∞, 0]. Under some hypotheses concerning the roots ofdet
where
is the Laplace transform of B(t), the asymptotic behavior of y(t) is discussed. Two typical results are: Theorem 3.1: suppose
∥B(t)∥ ɛ L1[0, ∞),
thendet
forRe λ>0 iff for every ɛ>0 there is an Mɛ>0 such that ∥Ttf∥l ⩽ ⩽ Mɛ
exp [ɛt]∥f∥l for t ⩾ 0. Corollary 3.1.1: suppose
exp [at]B(t) ∈ ∈ L1[0, ∞) for some a>0 anddet
forRe λ>−a. Then the solution of(L) is exponentially asymptotically stable.
Entrata in Redazione il 21 marzo 1975.
The author is grateful to ProfessorC. Corduneanu for suggesting this problem and for many helpful discussions during the preparation of the paper. 相似文献
3.
Sergio Campanato 《Annali di Matematica Pura ed Applicata》1970,86(1):125-154
Riassunto Si considera un'equazione ellittica non variazionale
aaDau=f a coefficienti continui in un apertogW di ℝn e si dimostrano certe proprietà locali delle soluzioni forti dell'equazione medesima nell'ipotesi che f appartenga allo spazio
di Morrey L
2,λ(Ω) o allo spazio di John-Nirenberg ℰ(Ω). Analoga indagine è svolta supponendoΩ=ℝ
+
n
e supponendo che u verifichi sull'iperpiano xn=0 condizioni di Dirichlet omogenee.
Ricerca svolta nell'ambito dei Contratti di Ricerca del Comitato per la Matematica del C.N.R.
Entrata in Redazione il 17 febbraio 1970. 相似文献
4.
Summary The problem considered is that of maximizing
dt subject to x=G(x, y), x(0)=c, and0 ≤y≤x. An essentially new feature is determining in what regions y=x,0<y<x, and y=0. 相似文献
5.
Summary The purpose of this paper is to study the validity of the Paley inequality on square function, for noncommutative martingales.
Let
be a regular gage space, and
a sequence of von-Neumann algebras such that
we prove that for every
, where ɛn(F) is the conditional expectation of F with respect to the subalgebra
: We also consider the case of a martingale arising in the context of harmonic analysis on noncommutative discrete groups,
in analogy to the theorem of R.E.A.C. Paley on Fourier-Walsh series.
Entrata in Redazione il 26 gennaio 1977.
Partially sponsored by C.N.R. 相似文献
6.
Wlodzimier Greblicki Miroslaw Pawlak 《Annals of the Institute of Statistical Mathematics》1985,37(1):443-454
Summary In the paper we estimate a regressionm(x)=E {Y|X=x} from a sequence of independent observations (X
1,Y
1),…, (X
n, Yn) of a pair (X, Y) of random variables. We examine an estimate of a type
, whereN depends onn andϕ
N is Dirichlet kernel and the kernel associated with the hermite series. Assuming, that E|Y|<∞ and |Y|≦γ≦∞, we give condition for
to converge tom(x) at almost allx, provided thatX has a density. if the regression hass derivatives, then
converges tom(x) as rapidly asO(nC−(2s−1)/4s) in probability andO(n
−(2s−1)/4s logn) almost completely. 相似文献
7.
8.
Summary Quaternion generalized fiber bundles
are studied, both isomorphic to global tensorial product
ordinary quaternion fiber bundles right and left respectively) and quite general ones. A cohomology class
is considered which represents the obstruction in order the fiber bundle be a tensorial product. Several properties and a
splitting principle are proved for bundles
. On this ground and founding on a convenient bundle BE → X associated to jaz (that we call Bonan's bundle and for which ɛ(
=ɛ(BE)) relations are stated among Stiefel-Whitney classes of
, BE and the class ɛ.
Entrata in Redazione il 14 agosto 1974.
Lavoro eseguito con contributo del C.N.R., nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni. 相似文献
Entrata in Redazione il 14 agosto 1974.
Lavoro eseguito con contributo del C.N.R., nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni. 相似文献
9.
W. A. Al-Salam 《Annali di Matematica Pura ed Applicata》1965,67(1):75-94
Summary In this paper we determine all orthogonal polynomials Un(x) such that Un(x)=x−1/2
F
2n+1
(x
1/2
) and
where f(t), u(t) have Taylor series expansions.
Supported in part by N. S. F. grant GP-1593. 相似文献
10.
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation
given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or
for some
Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝn must be infinite 相似文献
11.
Zheng Zukang 《数学学报(英文版)》1994,10(4):337-347
LetX
1,X
2, ...,X
n
be a sequence of nonnegative independent random variables with a common continuous distribution functionF. LetY
1,Y
2, ...,Y
n
be another sequence of nonnegative independent random variables with a common continuous distribution functionG, also independent of {X
i
}. We can only observeZ
i
=min(X
i
,Y
i
), and
. LetH=1−(1−F)(1−G) be the distribution function ofZ. In this paper, the limit theorems for the ratio of the Kaplan-Meier estimator
or the Altshuler estimator
to the true survival functionS(t) are given. It is shown that (1)P(δ(n)=1 i.o.)=0 ifF(τ
H
) < 1 andP(δ
n
=0 i.o. )=0 ifG(τH) > 1 where δ(n) is the corresponding indicator function of
and
have the same order
a.s., where {T
n
} is a sequence of constants such that 1−H(T
n
)=n
−α(logn)β(log logn)γ. 相似文献
12.
Cao Jiading 《分析论及其应用》1989,5(2):99-109
Let an≥0 and F(u)∈C [0,1], Sikkema constructed polynomials:
, ifα
n
≡0, then Bn (0, F, x) are Bernstein polynomials.
Let
, we constructe new polynomials in this paper:
Q
n
(k)
(α
n
,f(t))=d
k
/dx
k
B
n+k
(α
n
,F
k
(u),x), which are called Sikkema-Kantorovic polynomials of order k. Ifα
n
≡0, k=1, then Qn
(1) (0, f(t), x) are Kantorovič polynomials Pn(f). Ifα
n
=0, k=2, then Qn
(2), (0, f(t), x) are Kantorovič polynomials of second order (see Nagel). The main result is:
Theorem 2. Let 1≤p≤∞, in order that for every f∈LP [0, 1],
, it is sufficient and necessary that
,
§ 1. Let f(t) de a continuous function on [a, b], i. e., f∈C [a, b], we define[1–2],[8–10]:
.
As usual, for the space Lp [a,b](1≤p<∞), we have
and L[a, b]=l1[a, b].
Letα
n
⩾0and F(u)∈C[0,1],Sikkema-Bernstein polynomials
[3] [4].
The author expresses his thanks to Professor M. W. Müller of Dortmund University at West Germany for his supports. 相似文献
13.
In this paper, we use Laguerre calculus to find theLP spectrum (λ, Μ) of the pair (L, iT). Here
md T = ∂/∂t with
a basis for the left-invariant vector fields on the Heisenberg group. We find kernels for the spectral projection operators
on the ray λ > 0 in the Heisenberg brush and show that they are Calderón-Zygmund-Mikhlin operators. Estimates for these operators
in L
k
p
(Hn), HP(Hn), and S
k
pv
(Hn) spaces can therefore be deduced. 相似文献
14.
Michel Talagrand 《Israel Journal of Mathematics》1999,111(1):275-284
Consider the discrete cube Ω={0,1}
N
, provided with the uniform probabilityP. We denote byd(x, A) the Hamming distance of a pointx of Ω and a subsetA of Ω. We define the influenceI(A) of theith coordinate onA as follows. Forx in Ω, consider the pointT
i
(x) obtained by changing the value of theith coordinate. Then
We prove that we always have
Since it is easy to see that
, this recovers the well known fact that ∫Ω
d(x, A)dP(x) is at most of order
whenP(A)≥1/2. The new information is that ∫Ω
d(x, A)dP(x) can be of order
only ifA reassembles the Hamming ball {x; ∑1≤N
x
i
≥N/2}. 相似文献
15.
V. V. Andrievskii 《Journal d'Analyse Mathématique》2005,96(1):283-295
LetG⊂C be a quasidisk,K ⊂ G be a compact set, andp
n be a non-constant complex polynomial of degree at mostn. We establish the inequality
whereα
n < 0 depends onn, K,
and the geometrical structure of ϖG. 相似文献
16.
Given a sequence x of points in the unit interval, we associate with it a virtual permutation w=w(x) (that is, a sequence
w of permutationsw
n
such that for all n=1,2,..., wn−1=w′n is obtained from wn by removing the last element n from its cycle). We introduce a detailed version of the well-known stick breaking process
generating a random sequence x. It is proved that the associated random virtual permutation w(x) has a Ewens distribution.
Up to subsets of zero measure, the space
of virtual permutations is identified with the cube [0, 1]∞. Bibliography: 8 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 223, 1995, pp. 162–180. 相似文献
17.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2002,51(3):403-410
Let
be a sequence of positive numbers and 1≤p<∞. We consider the spaceH
p(β) of all power series
such that Σ|
(n)|p β(n
p<∞. We investigate regions on which our formal power series represent bounded analytic functions.
Research partially supported by the Shiraz University Research Council Grant No. 79-SC-1311-675. 相似文献
18.
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
19.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2000,49(1):115-120
Let
be a sequence of positive numbers and 1 ≤p < ∞. We consider the spacel
P(β) of all power series
such that
. We give a necessary and sufficient condition for a polynomial to be cyclic inl
P(β) and a point to be bounded point evaluation onl
P(β). 相似文献
20.
Francesco Leonetti 《Annali dell'Universita di Ferrara》1985,31(1):169-184
Riassunto In questo lavoro si prova la regolarità h?lderiana delle derivate, fino all'ordinek, dei minimi locali
dei funzionali
sotto opportune ipotesi suA
ij
αβ
e sug.
Summary In this paper we prove h?lder-continuity of the derivates, up to orderk, of local minima of functionals under suitable hypotheses forA ij αβ andg.相似文献