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New Paley–Wiener Theorems

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Abstract

In this paper, for an arbitrary fixed compact set K, we find necessary and sufficient conditions on the Taylor expansion coefficients of entire functions of exponential type so that these functions are the Fourier image of distributions supported in K. In other words, we state the Paley–Wiener theorem in the language of Taylor expansion coefficients.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2018.300.

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Authors and Affiliations

  1. Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet Street, Cau Giay, Hanoi, Vietnam

    Ha Huy Bang

  2. Department of Mathematics, College of Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Vu Nhat Huy

  3. Department of Mathematics, Thang Long Institute of Mathematics and Applied Sciences, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam

    Vu Nhat Huy

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  1. Ha Huy Bang
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Correspondence to Vu Nhat Huy.

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Bang, H.H., Huy, V.N. New Paley–Wiener Theorems. Complex Anal. Oper. Theory 14, 47 (2020). https://doi.org/10.1007/s11785-020-01005-2

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