Abstract
We analyze the following average sampling problem: Let h be a nonnegative measurable function supported in \(\big [-\frac{1}{2},\frac{1}{2}\big ].\) Given a sequence of samples \(\{y_{n}\}_{n \in {\mathbb {Z}}} \in {\mathbb {R}}^{{\mathbb {Z}}}\) of polynomial growth, find a multiply generated spline f of polynomial growth such that \(\int _{-\frac{1}{2}}^{\frac{1}{2}} f(n-t)h(t)dt = y_{n}\) , \(n \in {\mathbb {Z}}.\) It is shown that the solution to this problem is unique over certain subspaces of the multiply generated spline space of polynomial growth.
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Acknowledgments
The authors thank Anna University, Chennai-25, India for providing the Anna Centenary Research fellowship to the second author to carry out this research work.
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Devaraj, P., Yugesh, S. (2015). Reconstruction of Multiply Generated Splines from Local Average Samples. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_5
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DOI: https://doi.org/10.1007/978-81-322-2485-3_5
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