Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers (1 − |ξ| − |η|)+ and we make some advances in this investigation. We obtain an optimal result concerning the boundedness of these means from L × L into L with minimal smoothness, i.e., any δ > 0, and we obtain estimates for other pairs of spaces for...

Let φ denote Euler’s phi function. For a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n 6 x such that q ∤ φ(n). Part of the analysis involves a careful study of the Euler-Kronecker constants for cyclotomic fields. In particular, we show that the Hardy-Littlewood conjecture about counts of prime k-tuples and a conjecture o...

In this paper, we study a compound Korteweg-de Vries-Burgers equation with a higher-order nonlinearity. A class of solitary wave solutions is obtained by means of a series expansion.

We justify the holomorphic perturbation for the 1particle Inozemtsev model from the trigonometric model and show the holomorphy of the eigenvalues and the eigenfuncions which are obtained by the series expansion. We investigate the relationship between the L 2 space and the nite dimensional space of certain elliptic functions, and determine the distribution of the \algebraic" eigenvalues on the...

A new method of summation of slowly convergent series is proposed. It may be successfully applied to the summation of generalized and basic hypergeometric series, as well as some classical orthogonal polynomial series expansions. In some special cases, our algorithm is equivalent to Wynn’s epsilon algorithm, Weniger transformation (Computer Physics Reports 10 (1989) 189371) or the technique rec...

and Applied Analysis 3 Theorem 5. If u(x, t) = f(x)g(t), function f(x) = xh(x), where λ > −1 and h(x) has the generalized Taylor series expansion h(x) = ∑∞ n=0 a n (x − x 0 ) αn, (i) β < λ + 1 and α arbitrary, or (ii) β ≥ λ+1, α arbitrary, and a n = 0 for n = 0, 1, . . . , m− 1, wherem − 1 < β ≤ m, then the generalized differential transform (8) becomes U α,β (k, h) = 1 Γ (αk + 1) Γ (βh + 1) [D...

It is shown that the initial value problem (IVP) of the generalized KdV equation @tu + @x(a(u)) + @ 3 xu = 0; u(x; 0) = (x) is well posed in the classical Sobolev space H(R) with s > 3=4, which thus establishes a nonlinear map K from H(R) to C([ T; T ];H(R)). Then it is proved that (i) if a = a(x) is a C function on R to R, then K is in nitely many times Frechet di erentiable; (ii) if a = a(x) ...

This paper presents analysis and design results for control systems subject to oscillatory inputs, i.e., inputs of large amplitude and high frequency. The key analysis results are a series expansion characterizing the averaged system and various Lie-algebraic conditions that guarantee the series can be summed. Various example systems provide insight into the results. With regards to design, we ...

We simulated the fourier transform of the correlation function of the Ising model in two and three dimensions using a single cluster algorithm with improved estimators. The simulations are in agreement with series expansion and the available exact results in d = 2, which shows, that the cluster algorithm can succesfully be applied for correlations. We show as a further result that our data do n...

Various techniques are used to simplify the derivations of``greeks'' of path-independent claims in the Black±Merton±Scholes model. First, delta, gamma, speed, and other higher-order spatial derivatives of these claims are interpreted as the values of certain quantoed contingent claims. It is then shown that all partial derivatives of such claims can be represented in terms of these spatial deri...