Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 1273486
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] L. Autret, Entire vectors and time reversible Cauchy problems, Semigroup Forum 46 (1993), 347-351. MR 1206212 (93m:47046)
  • [2] R. deLaubenfels, Existence families, functional calculi and evolution equations, Lecture Notes in Math., vol. 1570, Springer-Verlag, New York, 1994. MR 1290783 (96b:47047)
  • [3] J. A. Goldstein, Semigroups of operators and applications, Oxford Univ. Press, New York, 1985. MR 790497 (87c:47056)
  • [4] R. Goodman, Complex Fourier analysis on a nilpotent Lie group, Trans. Amer. Math. Soc. 160 (1971), 373-391. MR 0417334 (54:5390)
  • [5] T. Kato, Perturbation theory for linear operators, Springer-Verlag, New York, 1966. MR 0203473 (34:3324)
  • [6] E. Nelson, Analytic vectors, Ann. of Math. (2) 70 (1959), 572-615. MR 0107176 (21:5901)
  • [7] F. Riesz and B. Sz.-Nagy, Functional analysis, Ungar, New York, 1955. MR 0071727 (17:175i)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34G10, 35K22, 47D06, 47N20

Retrieve articles in all journals with MSC: 34G10, 35K22, 47D06, 47N20

Additional Information

Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society