We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, th...We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.展开更多
Based on the fact that the quantum mechanical version of Hankel transform kernel（the Bessel function） is just the transform between ｜q, r〉 and（s, r′｜, two induced entangled state representations are given, and ...Based on the fact that the quantum mechanical version of Hankel transform kernel（the Bessel function） is just the transform between ｜q, r〉 and（s, r′｜, two induced entangled state representations are given, and working with them we derive fractional squeezing-Hankel transform（FrSHT） caused by the operator e（-iα）（a1-a-2-＋a-1a-2）e-（-iπa2-a2）, which is an entangled fractional squeezing transform operator. The additive rule of the FrSHT can be explicitly proved.展开更多
The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel ...The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel operators h(Phi) are presented in terms of a certain integral transform of the symbol Phi.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 10674045 and 60538010)the National Natural Science Foundation of Hunan Province,China (Grant No 08jj3001)
文摘We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.
基金Project supported by the National Natural Science Foundation of China(Grant No.11304126)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20130532)
文摘Based on the fact that the quantum mechanical version of Hankel transform kernel（the Bessel function） is just the transform between ｜q, r〉 and（s, r′｜, two induced entangled state representations are given, and working with them we derive fractional squeezing-Hankel transform（FrSHT） caused by the operator e（-iα）（a1-a-2-＋a-1a-2）e-（-iπa2-a2）, which is an entangled fractional squeezing transform operator. The additive rule of the FrSHT can be explicitly proved.
文摘The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel operators h(Phi) are presented in terms of a certain integral transform of the symbol Phi.
