Let f∈L p (R), 1≤p≤t8, and c j be the inner product of f and the Hermite function h j . Assume that c j 's satisfy $\left| {c_j } \right| \cdot f = o\left( 1 \right)\;\quad as\;j \to \infty $ If r=5/4, then the...Let f∈L p (R), 1≤p≤t8, and c j be the inner product of f and the Hermite function h j . Assume that c j 's satisfy $\left| {c_j } \right| \cdot f = o\left( 1 \right)\;\quad as\;j \to \infty $ If r=5/4, then the Hermite series Σc j h j conerges to f almost everywhere. If r=9/4-1/p, the Σ c j h j converges to f in L p (R).展开更多
In this study, we establish an approximate method which produces an approximate Hermite polynomial solution to a system of fractional order differential equations with variable coefficients. At collocation points, thi...In this study, we establish an approximate method which produces an approximate Hermite polynomial solution to a system of fractional order differential equations with variable coefficients. At collocation points, this method converts the mentioned system into a matrix equation which corresponds to a system of linear equations with unknown Hermite polynomial coefficients. Construction of the method on the aforementioned type of equations has been presented and tested on some numerical examples. Results related to the effectiveness and reliability of the method have been illustrated.展开更多
In this paper, we prove that under some restricted conditions, the non-bandiimited functions can be reconstructed by the multidimensional sampling theorem of Hermite type in the space of Lp（R^n）, 1 〈 p 〈 ∞.
文摘Let f∈L p (R), 1≤p≤t8, and c j be the inner product of f and the Hermite function h j . Assume that c j 's satisfy $\left| {c_j } \right| \cdot f = o\left( 1 \right)\;\quad as\;j \to \infty $ If r=5/4, then the Hermite series Σc j h j conerges to f almost everywhere. If r=9/4-1/p, the Σ c j h j converges to f in L p (R).
文摘In this study, we establish an approximate method which produces an approximate Hermite polynomial solution to a system of fractional order differential equations with variable coefficients. At collocation points, this method converts the mentioned system into a matrix equation which corresponds to a system of linear equations with unknown Hermite polynomial coefficients. Construction of the method on the aforementioned type of equations has been presented and tested on some numerical examples. Results related to the effectiveness and reliability of the method have been illustrated.
基金the National Natural Science Foundation of China （No. 10671019） Research Project of Science and Technology of Higher Education of Inner Mongolia （No. NJzy08163） Research Project of Education Bureau of Zhejiang Province （No. 20070509）.
文摘In this paper, we prove that under some restricted conditions, the non-bandiimited functions can be reconstructed by the multidimensional sampling theorem of Hermite type in the space of Lp（R^n）, 1 〈 p 〈 ∞.
