Wiener's lemma for twisted convolution and Gabor frames

We prove non-commutative versions of Wiener's Lemma on absolutely convergent Fourier series (a) for the case of twisted convolution and (b) for rotation algebras. As an application we solve some open problems about Gabor frames, among them the problem of Feichtinger and Janssen that is known in the literature as the ``irrational case'.

     

Convolution Quadrature Revisited

This article reviews convolution quadrature and its uses, extends the known approximation results for the case of sectorial Laplace transforms to finite-part convolutions with non-integrable kernel, and gives new, unified proofs of the optimal error bounds for both locally integrable and non-integrable convolution kernels.     

Complex-exponential representation of time-domain response of a one-mode resonator

Time-domain response of a one-mode resonator is investigated by using a complex-exponential representation of the time-domain impulse response. The transient response of a resonator has calculated for a short incident pulse which has rectangular form and the radio frequency filling. The convolution integral has been analytically carried out and two solutions for the time histories of the transient response of the resonator have been found. They are the early-time and late-time portions of the signal. The behaviour of amplitude and frequency of the transient response of the electrodynamical structure under consideration is studied.     

Continuity of convolution semigroups on hypergroups

LetK be a commutative hypergroup with the property that either the identity character is contained in the support of the Plancherel measure onK ^{^}, or the identity character is not isolated inK ^{^} and all characters sufficiently close (but not equal) to the identity character vanish at infinity. We present a shift compactness theorem forK and use this to prove that every symmetric convolution semigroup of probability measures onK is continuous.     

CONVOLUTION EQUATIONS WITH REFLECTION AND TRANSLATION SHIFT

（路见可）ＣＯＮＶＯＬＵＴＩＯＮＥＱＵＡＴＩＯＮＳＷＩＴＨＲＥＦＬＥＣＴＩＯＮＡＮＤＴＲＡＮＳＬＡＴＩＯＮＳＨＩＦＴ￥ＬｕＪｉａｎｋｅ（ＤｅｐｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００７２，Ｃｈｉｎａ）Ａｂｓｔｒ...     

Convolution products of nonidentical distributions on a topological semigroup

In this paper we present a number of sufficient conditions on a sequence of probability measuresµ _n on a locally compact (second countable) Hausdorff topological semigroupS that guarantee the weak convergence of the sequence of convolution productsµ _k,n µ _{k + 1} *···*µ _n (k), asn, for allk0.     

A restriction theorem associated with the generalized Sublaplacian

In this paper, we investigate the generalized Sublaplacian. We give the expression of the restriction operators explicitly. By introducing the generalized -twisted convolutions, we obtain the estimates of the restriction operators in the mixedL ^p spaces. Finally, we get a restriction theorem associated with the generalized Sublaplacian.     

重叠伏安峰的样条卷积法分辨

建立了分辨重叠峰的样条卷积法；利用三阶样条函数构成的峰分辨函数与原信号进行卷积，直接对重叠的伏安峰进行处理，取得了较好的结果；被处理的重叠峰可达到其线分离，且峰位置的相对误差小于3．0％（完全重叠峰为5．4％），峰面积的相对误差小于2．0％；应用于镉（Ⅱ）－铟（Ⅲ）实验体系的微分脉冲伏安信号处理，取得满意的结果。