In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequen...In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.展开更多
The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic fu...The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.展开更多
In this paper, we use the global search characteristics of genetic algorithms to help search the weight space of the neurons in the cascade-correlation architecture. The cascade-correlation learning architecture is a ...In this paper, we use the global search characteristics of genetic algorithms to help search the weight space of the neurons in the cascade-correlation architecture. The cascade-correlation learning architecture is a technique of training and building neural networks that starts with a simple network of neurons and adds additional neurons as they are needed to suit a particular problem. In our approach, instead ofmodifying the genetic algorithm to account for convergence problems, we search the weight-space using the genetic algorithm and then apply the gradient technique of Quickprop to optimize the weights. This hybrid algorithm which is a combination of genetic algorithms and cascade-correlation is applied to the two spirals problem. We also use our algorithm in the prediction of the cyclic oxidation resistance of Ni- and Co-base superalloys.展开更多
基金Supported by the National Natural Science Foundation of China(12301101)the Guangdong Basic and Applied Basic Research Foundation(2022A1515110019 and 2020A1515110585)。
文摘In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.
基金Supported by Natural Science Foundation of Guangdong Province in China(2018KTSCX161)。
文摘The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.
文摘In this paper, we use the global search characteristics of genetic algorithms to help search the weight space of the neurons in the cascade-correlation architecture. The cascade-correlation learning architecture is a technique of training and building neural networks that starts with a simple network of neurons and adds additional neurons as they are needed to suit a particular problem. In our approach, instead ofmodifying the genetic algorithm to account for convergence problems, we search the weight-space using the genetic algorithm and then apply the gradient technique of Quickprop to optimize the weights. This hybrid algorithm which is a combination of genetic algorithms and cascade-correlation is applied to the two spirals problem. We also use our algorithm in the prediction of the cyclic oxidation resistance of Ni- and Co-base superalloys.
