Abstract
The theory of Hilbert spaces of entire functions was conceived as a generalization of Fourier analysis by its founder, Louis de Branges. The Paley–Wiener spaces provided the motivating example. This chapter outlines the early development of the theory, showing how key steps were guided by the Hamburger moment problem, matrix differential equations, and eigenfunction expansions.
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Rovnyak, J. (2015). Hilbert Spaces of Entire Functions: Early History. In: Alpay, D. (eds) Operator Theory. Springer, Basel. https://doi.org/10.1007/978-3-0348-0667-1_8
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DOI: https://doi.org/10.1007/978-3-0348-0667-1_8
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