共查询到20条相似文献,搜索用时 15 毫秒
1.
G. A. Kalyabin 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):137-142
Explicit formulas are obtained for the maximum possible values of the derivatives f
(k)(x), x ∈ (−1, 1), k ∈ {0, 1, ..., r − 1}, for functions f that vanish together with their (absolutely continuous) derivatives of order up to ≤ r − 1 at the points ±1 and are such that $
\left\| {f^{\left( r \right)} } \right\|_{L_2 ( - 1,1)} \leqslant 1
$
\left\| {f^{\left( r \right)} } \right\|_{L_2 ( - 1,1)} \leqslant 1
. As a corollary, it is shown that the first eigenvalue λ
1,r
of the operator (−D
2)
r
with these boundary conditions is $
\sqrt 2
$
\sqrt 2
(2r)! (1 + O(1/r)), r → ∞. 相似文献
2.
Let $
\mathfrak{S}
$
\mathfrak{S}
be a locally compact semigroup, ω be a weight function on $
\mathfrak{S}
$
\mathfrak{S}
, and M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) be the weighted semigroup algebra of $
\mathfrak{S}
$
\mathfrak{S}
. Let L
0∞ ($
\mathfrak{S}
$
\mathfrak{S}
; M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)) be the C*-algebra of all M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)-measurable functions g on $
\mathfrak{S}
$
\mathfrak{S}
such that g/ω vanishes at infinity. We introduce and study a strict topology β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω) on M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) and show that the Banach space L
0∞ ($
\mathfrak{S}
$
\mathfrak{S}
; M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω)) can be identified with the dual of M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω) endowed with β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω). We finally investigate some properties of the locally convex topology β
1($
\mathfrak{S}
$
\mathfrak{S}
, ω) on M
a
($
\mathfrak{S}
$
\mathfrak{S}
, ω). 相似文献
3.
V. I. Gorbachuk V. M. Gorbachuk 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(2):114-121
Let A be a closed linear operator on a Banach space $
\mathfrak{B}
$
\mathfrak{B}
over the field Ω of complex p-adic numbers having an inverse operator defined on the whole $
\mathfrak{B}
$
\mathfrak{B}
, and f be a locally holomorphic at 0 $
\mathfrak{B}
$
\mathfrak{B}
-valued vector function. The problem of existence and uniqueness of a locally holomorphic at 0 solution of the differential
equation y
(m) − Ay = f is considered in this paper. In particular, it is shown that this problem is solvable under the condition $
\mathop {\lim }\limits_{n \to \infty } \sqrt[n]{{\left\| {A^{ - n} } \right\|}}
$
\mathop {\lim }\limits_{n \to \infty } \sqrt[n]{{\left\| {A^{ - n} } \right\|}}
= 0. It is proved also that if the vector-function f is entire, then there exists a unique entire solution of this equation. Moreover, the necessary and sufficient conditions
for the Cauchy problem for such an equation to be correctly posed in the class of locally holomorphic functions are presented. 相似文献
4.
A. A. Mogul’skiĭ 《Siberian Advances in Mathematics》2010,20(3):191-200
Let X,X(1),X(2),... be independent identically distributed random variables with mean zero and a finite variance. Put S(n) = X(1) + ... + X(n), n = 1, 2,..., and define the Markov stopping time η
y
= inf {n ≥ 1: S(n) ≥ y} of the first crossing a level y ≥ 0 by the random walk S(n), n = 1, 2,.... In the case $
\mathbb{E}
$
\mathbb{E}
|X|3 < ∞, the following relation was obtained in [8]: $
\mathbb{P}\left( {\eta _0 = n} \right) = \frac{1}
{{n\sqrt n }}\left( {R + \nu _n + o\left( 1 \right)} \right)
$
\mathbb{P}\left( {\eta _0 = n} \right) = \frac{1}
{{n\sqrt n }}\left( {R + \nu _n + o\left( 1 \right)} \right)
as n → ∞, where the constant R and the bounded sequence ν
n
were calculated in an explicit form. Moreover, there were obtained necessary and sufficient conditions for the limit existence
$
H\left( y \right): = \mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _y = n} \right)
$
H\left( y \right): = \mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _y = n} \right)
for every fixed y ≥ 0, and there was found a representation for H(y). The present paper was motivated by the following reason. In [8], the authors unfortunately did not cite papers [1, 5] where
the above-mentioned relations were obtained under weaker restrictions. Namely, it was proved in [5] the existence of the limit
$
\mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _y = n} \right)
$
\mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _y = n} \right)
for every fixed y ≥ 0 under the condition
$
\mathbb{E}
$
\mathbb{E}
X
2 < ∞ only; In [1], an explicit form of the limit $
\mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _0 = n} \right)
$
\mathop {\lim }\limits_{n \to \infty } n^{{3 \mathord{\left/
{\vphantom {3 2}} \right.
\kern-\nulldelimiterspace} 2}} \mathbb{P}\left( {\eta _0 = n} \right)
was found under the same condition
$
\mathbb{E}
$
\mathbb{E}
X
2 < ∞ in the case when the summand X has an arithmetic distribution. In the present paper, we prove that the main assertion in [5] fails and we correct the original proof. It worth noting that
this corrected version was formulated in [8] as a conjecture. 相似文献
5.
A. A. Yukhimenko 《Moscow University Mathematics Bulletin》2010,65(2):69-71
The system of exponents $
\left\{ {e^{i\lambda _n t} } \right\}_{n \in \mathbb{Z}}
$
\left\{ {e^{i\lambda _n t} } \right\}_{n \in \mathbb{Z}}
is considered. A sufficient condition for a Riesz-property basis in the weighted space L
p
(−π, π) is obtained. 相似文献
6.
Horst Alzer 《Proceedings Mathematical Sciences》2010,120(2):131-137
Let n ≥ 1 be an integer and let P
n
be the class of polynomials P of degree at most n satisfying z
n
P(1/z) = P(z) for all z ∈ C. Moreover, let r be an integer with 1 ≤ r ≤ n. Then we have for all P ∈ P
n
:
$
\alpha _n (r)\int_0^{2\pi } {|P(e^{it} )|^2 dt} \leqslant \int_0^{2\pi } {|P^r (e^{it} )|^2 dt} \leqslant \beta _n (r)\int_0^{2\pi } {|P(e^{it} )|^2 dt}
$
\alpha _n (r)\int_0^{2\pi } {|P(e^{it} )|^2 dt} \leqslant \int_0^{2\pi } {|P^r (e^{it} )|^2 dt} \leqslant \beta _n (r)\int_0^{2\pi } {|P(e^{it} )|^2 dt}
相似文献
7.
Let λ be a real number such that 0 < λ < 1. We establish asymptotic formulas for the weighted real moments Σ
n≤x
R
λ
(n)(1 − n/x), where R(n) =$
\prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu - 1} }
$
\prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu - 1} }
is the Atanassov strong restrictive factor function and n =$
\prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu } }
$
\prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu } }
is the prime factorization of n. 相似文献
8.
In this paper,we obtain the boundedness of the parabolic singular integral operator T with kernel in L(logL)1/γ(Sn-1) on Triebel-Lizorkin spaces.Moreover,we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q(f) from ∥f∥ F˙p0,q(Rn) into Lp(Rn). 相似文献
9.
Zamira Abdikalikova Ryskul Oinarov Lars-Erik Persson 《Czechoslovak Mathematical Journal》2011,61(1):7-26
We consider a new Sobolev type function space called the space with multiweighted derivatives $
W_{p,\bar \alpha }^n
$
W_{p,\bar \alpha }^n
, where $
\bar \alpha
$
\bar \alpha
= (α
0, α
1,…, α
n
), α
i
∈ ℝ, i = 0, 1,…, n, and $
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
$
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
,
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