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Mathematics, Number Theory, Functional Analysis
Abstract:
In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set $\{0,\pm\sqrt{1}, \pm\sqrt{2}, \pm\sqrt{3},\dots\}$. The functions in the interpolating basis are constructed in a closed form as an integral transform of weakly holomorphic modular forms for the theta subgroup of the modular group.
