Abstract
For a linear differential-difference equation with real shifts in the complex plane we prove a theorem of existence of entire solutions for an arbitrary entire function in the r.h.s. and, using it, show that the space of entire solutions of the corresponding homogeneous equation is infinite dimensional.
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To the memory of Moshe Livshits
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Belitskii, G., Tkachenko, V. (2009). Differential-difference Equations in Entire Functions. In: Alpay, D., Vinnikov, V. (eds) Characteristic Functions, Scattering Functions and Transfer Functions. Operator Theory: Advances and Applications, vol 197. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0183-2_1
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DOI: https://doi.org/10.1007/978-3-0346-0183-2_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0182-5
Online ISBN: 978-3-0346-0183-2
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