Banach空间的型与独立Banach空间值随机变量序列的不等式

本文建立了独立Ｂ值随机变量序列部分和的极大值函数Ｓ＊与ｐ方根函数Ｓ（ｐ，Ｘ）的分布函数不等式与矩不等式，讨论了这些不等式的成立与Ｂａｎａｃｈ空间的ｐ型与ｑ余型的关系，同时给出了与Ｈｉｌｂｅｒｔ空间同构的Ｂａｎａｃｈ空间的特征。     

多圆柱上Bergman空间到Bloch空间的复合算子

设qo是单位多圆柱Dn到自身的—个全纯映射,ψ是Dn上的—个全纯函数．本文研究单位多圆柱上从Bergman空间Ap（Dn）到Bloch空间β（Dn）的加权复合算子Tψ,ψ通过全纯映射ψ和全纯函数ψ的函数特征。分别给出了单位多圆柱上从Bergman空间AP（Dn）到Bloch空间β（Dn）的加权复合算子Tψ,ψ有界性和紧性的充分必要条件．     

Banach空间中的Rosenthal型不等式及其应用

分别对Banach空间值鞅差序列和独立随机变量序列证明了Rosenthal型不等式,所得结论揭示了Rosenthal型不等式与Banach空间的p型、q余型、p一致光滑性和q一致凸性之间的内在联系.     

Clarkson不等式与Banach空间几何

我们证明了Banach空间X是Clarkson p型（q余型）当且仅当X是一个特殊的p一致光滑空间（q-一致凸空间（）,我们还找到刻划型（余型）的一系列鞅不等式,同时,我们得到了均方函数sharp不等式。     

Cn单位球上的向量值D函数

讨论了Cn单位球上的向量值Dpμ,q函数, 利用Banach空间几何学的方法,推广了标量值Dpμ,q函数的结果.     

Cn单位球上的向量值Dpμ,q函数

讨论了Cn单位球上的向量值Dpμ,q函数, 利用Banach空间几何学的方法,推广了标量值Dpμ,q函数的结果.     

型和余型的一个解析鞅特征

应用解析鞅的不等式及其收敛性给出了Ｂａｎａｃｈ空间的型和余型的刻划．     

Morrey型空间刻画和Carleson测度

定义了解析Morrey型空间H_K~p,并利用H~p空间范数给出了其刻画.还运用Carleson测度刻画了从H_K~p到帐篷型空间J_K~p(μ)嵌入映射的有界性及紧性,其中,权函数K:[0,∞)→[0,∞)是一个右连续且非递减的函数.     

单位球上F(p,q,s)到μ-Bloch空间的点乘子

设μ是正规函数,文中探讨了多复变中单位球上一般函数空间F(p,q,s)到广义Bloch型空间β_μ的点乘子,并给出了几个推论.     

C~n 单位球上的向量值D_(μ,q)~q 函数(英文)

讨论了Cn 单位球上的向量值Dpμ,q函数, 利用Banach空间几何学的方法,推广了标量值 Dpμ,q函数的结果。     

An Identity Relating a Theta Function to a Sum of Lambert Series

We derive an identity connecting a theta function and a sumof Lambert series. As a consequence of this identity, we deducea number of results of Jacobi, Dirichlet, Lorenz, Ramanujanand Rademacher.     

Reciprocity formulae for multiple Dedekind–Rademacher sums

We introduce multiple Dedekind–Rademacher sums, in terms of values of Bernoulli functions, that generalize the classical Dedekind–Rademacher sums. The aim of this paper is to give and prove a reciprocity law for these sums. The main theorem presented in this paper contains all previous results in the literature about Dedekind–Rademacher sums.     

Algorithmically random series and Brownian motion

We consider some random series parametrised by Martin-Löf random sequences. The simplest case is that of Rademacher series, independent of a time parameter. This is then extended to the case of Fourier series on the circle with Rademacher coefficients. Finally, a specific Fourier series which has coefficients determined by a computable function is shown to converge to an algorithmically random Brownian motion.     

Rademacher's infinite partial fraction conjecture is (almost certainly) false

In his book Topics in Analytic Number Theory, Hans Rademacher conjectured that the limits of certain sequences of coefficients that arise in the ordinary partial fraction decomposition of the generating function for partitions of integers into at most N parts exist and equal particular values that he specified. Despite being open for nearly four decades, little progress has been made towards proving or disproving the conjecture, perhaps in part due to the difficulty in actually computing the coefficients in question. In this paper, we present a recurrence (alias difference equation) which provides a fast algorithm for calculating the Rademacher coefficients, a large amount of data, direct formulae for certain collections of Rademacher coefficients, and overwhelming evidence against the truth of the conjecture. While the limits of the sequences of Rademacher coefficients do not exist (the sequences oscillate and attain arbitrarily large positive and negative values), the sequences do get very close to Rademacher's conjectured limits for certain (predictable) indices in the sequences.     

Asymptotic sequential Rademacher complexity of a finite function class

For a finite function class, we describe the large sample limit of the sequential Rademacher complexity in terms of the viscosity solution of a G-heat equation. In the language of Peng’s sublinear expectation theory, the same quantity equals to the expected value of the largest order statistics of a multidimensional G-normal random variable. We illustrate this result by deriving upper and lower bounds for the asymptotic sequential Rademacher complexity.     

An analogue of the Dedekind–Rademacher sum and certain ray class invariants of real quadratic fields

In this paper, we consider a certain product of double sine functions as an analogue of the Dedekind–Rademacher sum. Its reciprocity formulas are established by decomposition of a certain double zeta function. As their applications, we reconstruct and refine a part of Arakawa?s work on ray class invariants of real quadratic fields, and prove directly explicit relations between various invariants which are defined in terms of the double sine function and are related to the Stark–Shintani conjecture. Moreover, in some examples, new expressions of the invariants are revealed. As two appendices, we give a new proof of Carlitz?s three-term relation for the Dedekind–Rademacher sum and a simple proof of Arakawa?s transformation formula for an analogue of the generalized Eisenstein series originated with Lewittes.     

The Rademacher conjecture and <Emphasis Type="Italic">q</Emphasis>-partial fractions

In his classic book, Topics in Analytic Number Theory, H. Rademacher posed a natural conjecture concerning the generating function for p(n), the number of partitions of n. In this paper we undertake a systematic study of an expansion technique that has its genesis in the work of Cayley. We apply this to the Rademacher conjecture, and obtain the first positive result providing theoretical evidence for the conjecture.      

Oracle inequalities for support vector machines that are based on random entropy numbers

In this paper, we present a new technique for bounding local Rademacher averages of function classes induced by a loss function and a reproducing kernel Hilbert space (RKHS). At the heart of this technique lies the observation that certain expectations of random entropy numbers can be bounded by the eigenvalues of the integral operator associated with the RKHS. We then work out the details of the new technique by establishing two new oracle inequalities for support vector machines, which complement and generalize previous results.     

Walsh函数的一种新定义及快速算法设计

传统的Walsh函数是以Rademacher函数为基函数生成 .本文运用对称复制的观点 ,定义了一种新函数 G函数 ,并以G函数为基础 ,定义了四种序的Walsh函数 ,同时 ,运用序码分析方法 ,实现了两种序Walsh变换的快速算法设计 .     

Vector-valued walsh-paley martingales and geometry of banach spaces

The concept of Rademacher typep (1≤p≤2) plays an important role in the local theory of Banach spaces. In [3] Mascioni considers a weakening of this concept and shows that for a Banach spaceX weak Rademacher typep implies Rademacher typer for allr<p. As with Rademacher typep and weak Rademacher typep, we introduce the concept of Haar typep and weak Haar typep by replacing the Rademacher functions by the Haar functions in the respective definitions. We show that weak Haar typep implies Haar typer for allr<p. This solves a problem left open by Pisier [5]. The method is to compare Haar type ideal norms related to different index sets.