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.     

一类紧半群上概率测度卷积幂的弱收敛性

本文讨论紧半群上概率测度卷积幂的弱收敛性，将紧群上的Ｋａｗａｄａ－Ｉｔ６型结果以相应的形式建立到一类紧半群上．本文的结论蕴含了［１］中的定理２．１．４与［２］中的定理１．     

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.     

Continuous and discrete Bessel wavelet transforms

Using the theory of Hankel convolution, continuous and discrete Bessel wavelet transforms are defined. Certain boundedness results and inversion formula for the continuous Bessel wavelet transform are obtained. Important properties of the discrete Bessel wavelet transform are given.     

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...     

On Infinitesimally Optimal Paths

The concept of infinitesimal optimality is specified for discrete dynamic extremal problems.     

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.