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Entire solutions of the abstract Cauchy problem in a Hilbert space


Authors: Ralph deLaubenfels and Fuyuan Yao
Journal: Proc. Amer. Math. Soc. 123 (1995), 3351-3356
MSC: Primary 34G10; Secondary 35K22, 47D06, 47N20
DOI: https://doi.org/10.1090/S0002-9939-1995-1273486-9
MathSciNet review: 1273486
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Abstract: We show that, whenever the linear operator A is symmetric and densely defined, on a Hilbert space, then the abstract Cauchy problem

$\displaystyle \frac{d}{{dz}}u(z) = {A^ \ast }(u(z))\quad (z \in {\mathbf{C}}),\qquad u(0) = x$

has an entire solution, for all initial data x in the image of $ {e^{ - \bar A{A^ \ast }}}$, which is a dense set.

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DOI: https://doi.org/10.1090/S0002-9939-1995-1273486-9
Article copyright: © Copyright 1995 American Mathematical Society