- 期刊
THE GENERALIZED SAMPLING THEOREM FOR TRANSFORMS OF NOT NECESSARILY SQUARE INTEGRABLE FUNCTIONS
並列摘要
It is known that the generalized sampling theorem is valid for certain finite limit integral transforms of square integrable functions. In this note, we will extend the validity of the theorem to include transforms of absolutely integrable functions associated with differentiable kernels. In the proof, we will use the Holder inequality and a known theorem concerning the uniform convergence of the orthogonal series to the differentiable kernel of the particular integral transform.
延伸閱讀
- Zapryanova, T., & Tachev, G. (2012). Generalized Inverse Theorem for Schoenberg Operator. Journal of Modern Mathematics Frontier, 1(2), 11-16. https://www.airitilibrary.com/Article/Detail?DocID=P20150611017-201206-201508170020-201508170020-11-16
- KROOPNICK, A. (1995). GENERAL BOUNDEDNESS THEOREMS TO SOME SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION WITH INTEGRABLE FORCING TERM. International Journal of Mathematics and Mathematical Sciences, 1995(), 823-824. https://doi.org/10.1155/S0161171295001050
- Garg, M., Manohar, P., & Kalla, S. L. (2011). Generalized Differential Transform Method to Space-Time Fractional Telegraph Equation. International Journal of Differential Equations, 2011(), 593-601. https://doi.org/10.1155/2011/548982
- Takizawa, E. (1975). On the Generalized Sampling Theorem, Generalized Frequency, and Generalized Band-Limited Spectrum Function. Chinese Journal of Physics, 13(2), 226-246. https://www.airitilibrary.com/Article/Detail?DocID=05779073-197510-201310090002-201310090002-226-246
- Lai, C. C. (2009). Some Iteration Methods for Solving Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory [master's thesis, National Tsing Hua University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0016-1111200916013271