共查询到20条相似文献,搜索用时 31 毫秒
1.
V. A. Yudin 《Proceedings of the Steklov Institute of Mathematics》2011,273(1):188-189
It is established that H. Bohr’s inequality \(\sum\nolimits_{k = 0}^\infty {\left| {{{f^{\left( k \right)} \left( 0 \right)} \mathord{\left/ {\vphantom {{f^{\left( k \right)} \left( 0 \right)} {\left( {2^{{k \mathord{\left/ {\vphantom {k 2}} \right. \kern-\nulldelimiterspace} 2}} k!} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {2^{{k \mathord{\left/ {\vphantom {k 2}} \right. \kern-\nulldelimiterspace} 2}} k!} \right)}}} \right| \leqslant \sqrt 2 \left\| f \right\|_\infty }\) is sharp on the class H ∞. 相似文献
2.
Forn a positive integer letp(n) denote the number of partitions ofn into positive integers and letp(n,k) denote the number of partitions ofn into exactlyk parts. Let
, thenP(n) represents the total number of parts in all the partitions ofn. In this paper we obtain the following asymptotic formula for
. 相似文献
3.
K. F. Cheng 《Periodica Mathematica Hungarica》1983,14(2):177-187
The nonparametric regression problem has the objective of estimating conditional expectation. Consider the model $$Y = R(X) + Z$$ , where the random variableZ has mean zero and is independent ofX. The regression functionR(x) is the conditional expectation ofY givenX = x. For an estimator of the form $$R_n (x) = \sum\limits_{i = 1}^n {Y_i K{{\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} \mathord{\left/ {\vphantom {{\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} {\sum\limits_{i = 1}^n {K\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} }}} \right. \kern-\nulldelimiterspace} {\sum\limits_{i = 1}^n {K\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} }}} $$ , we obtain the rate of strong uniform convergence $$\mathop {\sup }\limits_{x\varepsilon C} \left| {R_n (x) - R(x)} \right|\mathop {w \cdot p \cdot 1}\limits_ = o({{n^{{1 \mathord{\left/ {\vphantom {1 {(2 + d)}}} \right. \kern-\nulldelimiterspace} {(2 + d)}}} } \mathord{\left/ {\vphantom {{n^{{1 \mathord{\left/ {\vphantom {1 {(2 + d)}}} \right. \kern-\nulldelimiterspace} {(2 + d)}}} } {\beta _n \log n}}} \right. \kern-\nulldelimiterspace} {\beta _n \log n}}),\beta _n \to \infty $$ . HereX is ad-dimensional variable andC is a suitable subset ofR d . 相似文献
4.
In this paper, a number of problems concerning the uniform approximation of complex-valued continuous functions
on compact subsets of the complex plane by simplest fractions of the form
are considered. In particular, it is shown that the best approximation of a function
by the fractions
is of the same order of vanishing as the best approximations by polynomials of degree
. 相似文献
5.
We show that the zeros of the hypergeometric polynomials
,
, cluster on the loop of the lemniscate
as
. We also state the equations of the curves on which the zeros of
, lie asymptotically as
. Auxiliary results for the asymptotic zero distribution of other functions related to hypergeometric polynomials are proved,
including Jacobi polynomials with varying parameters and associated Legendre functions. Graphical evidence is provided using
Mathematica.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
Bruno Pini 《Annali di Matematica Pura ed Applicata》1959,48(1):305-332
Sunto Si studia il problema della determinazione di una soluzione dell'equazione
ak(x)∂ku/∂xk=f(x, y) entro la semistriscia a≤x≤b, y≥0, che assuma assegnati valori per y=0 e per x=a, x1, x2, b (a<x1<x2<b). Analogamente si studia il problema della determinazione di una soluzione dell' equazione
ak(x)∂ku/∂xk+b(x)∂u/∂y=f(x,y), entro la medesima semistriscia, cha assuma assegnati valori per y=0 e per x=a, x1, x2, b e la cui ∂/∂y assuma assegnati valori per y=0.
A Giovanni Sansone nel suo 70mo compleanno. 相似文献
7.
Let Θ be a bounded open set in ℝ
n
, n ⩾ 2. In a well-known paper Indiana Univ. Math. J., 20, 1077–1092 (1971) Moser found the smallest value of K such that
$
\sup \left\{ {\int_\Omega {\exp \left( {\left( {\frac{{\left| {f(x)} \right|}}
{K}} \right)^{{n \mathord{\left/
{\vphantom {n {(n - 1)}}} \right.
\kern-\nulldelimiterspace} {(n - 1)}}} } \right):f \in W_0^{1,n} (\Omega ),\left\| {\nabla f} \right\|_{L^n } \leqslant 1} } \right\} < \infty
$
\sup \left\{ {\int_\Omega {\exp \left( {\left( {\frac{{\left| {f(x)} \right|}}
{K}} \right)^{{n \mathord{\left/
{\vphantom {n {(n - 1)}}} \right.
\kern-\nulldelimiterspace} {(n - 1)}}} } \right):f \in W_0^{1,n} (\Omega ),\left\| {\nabla f} \right\|_{L^n } \leqslant 1} } \right\} < \infty
相似文献
8.
А. М. Седлетский 《Analysis Mathematica》1994,20(2):117-132
The paper is devoted to study the asymptotic behaviour of zerosz
n
of an entire function of Mittag-Leffler's type
|