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.
E. Bolthausen 《Probability Theory and Related Fields》1986,72(2):305-318
Summary LetX
i,iN, be i.i.d.B-valued random variables whereB is a real separable Banach space, and a mappingB R. Under some conditions an asymptotic evaluation of
is possible, up to a factor (1+o(1)). This also leads to a limit theorem for the appropriately normalized sums
under the law transformed by the density exp
. 相似文献
3.
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
0,\mu \in C.}}} \right. \kern-\nulldelimiterspace} {\Gamma (\mu + {n \mathord{\left/ {\vphantom {n \rho }} \right. \kern-\nulldelimiterspace} \rho }),\rho > 0,\mu \in C.}}}$$
" align="middle" vspace="20%" border="0"> 相似文献
4.
We obtain the new exact Kolmogorov-type inequality
5.
Forn a positive integer letp(n) denote the number of partitions ofn into positive integers and letp(n,k) denote the number of partitions ofn into exactlyk parts. Let
, thenP(n) represents the total number of parts in all the partitions ofn. In this paper we obtain the following asymptotic formula for
. 相似文献
6.
V. N. Chubarikov 《Mathematical Notes》1976,20(1):589-593
We obtain an estimate of the modulus of a complete multiple rational trigonometric sum: $$\left| {\sum {_{x_{1, \ldots ,} x_r = 1^{\exp \left( {{{2\pi if\left( {x_{1, \ldots ,} x_r } \right)} \mathord{\left/ {\vphantom {{2\pi if\left( {x_{1, \ldots ,} x_r } \right)} q}} \right. \kern-\nulldelimiterspace} q}} \right)} }^q } } \right| \ll q^{{{r - 1} \mathord{\left/ {\vphantom {{r - 1} {n + \varepsilon }}} \right. \kern-\nulldelimiterspace} {n + \varepsilon }}} ,$$ where $$\begin{gathered} f\left( {x_{1, \ldots ,} x_r } \right) = \sum {_{0 \leqslant t_1 , \ldots ,t_r \leqslant n^a t_1 , \ldots ,t_r x_1^{t_1 } \ldots x_r^{t_r } ,} } \hfill \\ a_{0, \ldots ,0} = 0,\left( {a_{0, \ldots ,0,1} , \ldots ,a_{n, \ldots ,n,} q} \right) = 1 \hfill \\ \end{gathered} $$ , and an estimate of the modulus of a multiple trigonometric integral. 相似文献
7.
V. A. Timorin 《Functional Analysis and Its Applications》2001,35(3):189-198
We study some combinatorial properties of polytopes that are simple at the edges. We give an elementary geometric proof of an analog of the hard Lefschetz theorem for the polytopes for which the distance between any two nonsimple vertices is sufficiently large. This implies that the h-vector of such polytopes satisfies the relations
, where d is the dimension of the polytope, which proves a special case of Stanley's conjecture. 相似文献
8.
The integral $$\int_0^{{\pi \mathord{\left/ {\vphantom {\pi 4}} \right. \kern-\nulldelimiterspace} 4}} {\ln \left( {\cos ^{{m \mathord{\left/ {\vphantom {m n}} \right. \kern-\nulldelimiterspace} n}} \theta \pm \sin ^{{m \mathord{\left/ {\vphantom {m n}} \right. \kern-\nulldelimiterspace} n}} \theta } \right)d\theta } $$ where m and n are relatively prime positive integers, is evaluated exactly in terms of elementary functions and the Catalan constant G. 相似文献
9.
Vincent Cachia Hagen Neidhardt Valentin A. Zagrebnov 《Integral Equations and Operator Theory》2002,42(4):425-448
LetA be a positive self-adjoint operator and letB be anm-accretive operator which isA-small with a relative bound less than one. LetH=A+B, thenH is well-defined on dom(H)=dom(A) andm-accretive. IfB is a strictlym-accretive operator obeying
10.
We study inequalities of the form $$ \tau (w(A)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} f(A)w(A)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} ) \leqslant \tau (w(A)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} f(B)w(A)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} ),A \leqslant B $$ where τ is a trace on a von Neumann algebra or a C*-algebra, A and B are self-adjoint elements of the algebra in question, f and w are real-valued functions, and the “weight” function w is nonnegative. 相似文献
11.
Summary LetX be a diffusion in natural scale on (0,1], with 1 reflecting, and letc(x)(H
x
) andv(x)var (H
x
), whereH
x
=inf{t: X
t
=x}. Let
x
=sup{t:X
t
=x}. The main results of this paper are firstly that (i)c is slowly varying; (ii)
are all equivalent: and secondly that (v)
are all equivalent, and are implied by the condition
. Other partial results for more general limit theorems are proved, and new results on regular variation are established. 相似文献
12.
A. E. Rudenok 《Differential Equations》2009,45(2):159-167
We suggest a new approach to studying the isochronism of the system 相似文献
${{dx} \mathord{\left/ {\vphantom {{dx} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} = - y + p_n (x,y),{{dy} \mathord{\left/ {\vphantom {{dy} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} = x + q_n (x,y),$ ${{dX} \mathord{\left/ {\vphantom {{dX} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} = - Y + XS(X,Y),{{dY} \mathord{\left/ {\vphantom {{dY} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} = X + YS(X,Y)$ 13.
Jeremy T. Tyson 《Potential Analysis》2006,24(4):357-384
We obtain sharp weighted Moser–Trudinger inequalities for first-layer symmetric functions on groups of Heisenberg type, and for -symmetric functions on the Grushin plane. To this end, we establish weighted Young's inequalities in the form , for first-layer radial weights on a general Carnot group and functions with first-layer symmetric. The proofs use some sharp estimates for hypergeometric functions.Research supported by NSF grant DMS-0228807. 相似文献
14.
15.
Tadej Kotnik 《Advances in Computational Mathematics》2008,29(1):55-70
The paper describes a systematic computational study of the prime counting function π(x) and three of its analytic approximations: the logarithmic integral \({\text{li}}{\left( x \right)}: = {\int_0^x {\frac{{dt}}{{\log \,t}}} }\), \({\text{li}}{\left( x \right)} - \frac{1}{2}{\text{li}}{\left( {{\sqrt x }} \right)}\), and \(R{\left( x \right)}: = {\sum\nolimits_{k = 1}^\infty {{\mu {\left( k \right)}{\text{li}}{\left( {x^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} } \right)}} \mathord{\left/ {\vphantom {{\mu {\left( k \right)}{\text{li}}{\left( {x^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} } \right)}} k}} \right. \kern-\nulldelimiterspace} k} }\), where μ is the Möbius function. The results show that π(x)
16.
We investigate the relationship between the constants K(R) and K(T), where
is the exact constant in the Kolmogorov inequality, R is the real axis, T is a unit circle,
17.
G. Kuba 《Acta Mathematica Hungarica》2001,91(4):325-332
For a large real parameter t and 0 a b
we consider sums
where is the rounding error function, i.e. (z) = z - [z] - 1/2. We generalize Huxley's well known estimate
by showing that
holds uniformly in 0 a b
. Fruther, we investigate an analogous question related to the divisor problem and show that the inequality
, which (due to Huxley) holds uniformly in 0 a b
, and which is in general not true for 1 a b t, is true uniformly in 0 a b
. 相似文献
18.
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
19.
Angelo Cavallucci 《Annali di Matematica Pura ed Applicata》1969,83(1):337-362
Sunto Si prova un teorema di tracce per spazi di funzioni, definite su R
+
n
, con norme del tipo
.
Entrata in Redazione il 23 luglio 1969.
Lavoro eseguito nell'ambito dei gruppi di ricerca del Comitato Nazionale per la Matematica del C.N.R. 相似文献
20.
D. Suryanarayana 《Periodica Mathematica Hungarica》1983,14(1):69-75
LetL(x) denote the number of square-full integers not exceedingx. It is well-known that $$L\left( x \right) \sim \frac{{\zeta \left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right)}}{{\zeta \left( 3 \right)}}x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + \frac{{\zeta \left( {{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} \right)}}{{\zeta \left( 2 \right)}}x^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} ,$$ whereζ(s) denotes the Riemann Zeta function, LetΔ(x) denote the error function in the asymptotic formula forL(x). On the assumption of the Riemann hypothesis (R.H.), it is known that $$\Delta x = O\left( {x^{13/81 + 8} } \right)$$ for everyε > 0. In this paper, we prove on the assumption of R.H. that $$\frac{1}{x}\int\limits_x^1 {\left| {\Delta \left( t \right)} \right|dt = O\left( {x^{1/10 + ^8 } } \right)} .$$ In fact, we prove a more general result. We conjecture that $$\Delta x = O\left( {x^{1/10 + ^8 } } \right)$$ under the assumption of the R.H. 相似文献
|