On analytic semigroups and cosine functions in Banach spaces

V. Keyantuo; P. Vieten

Studia Mathematica (1998)

  • Volume: 129, Issue: 2, page 137-156
  • ISSN: 0039-3223

Abstract

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If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform.

How to cite

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Keyantuo, V., and Vieten, P.. "On analytic semigroups and cosine functions in Banach spaces." Studia Mathematica 129.2 (1998): 137-156. <http://eudml.org/doc/216495>.

@article{Keyantuo1998,
abstract = {If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform.},
author = {Keyantuo, V., Vieten, P.},
journal = {Studia Mathematica},
keywords = {negative square root; holomorphic semigroup; conjugate potential transform of the cosine function},
language = {eng},
number = {2},
pages = {137-156},
title = {On analytic semigroups and cosine functions in Banach spaces},
url = {http://eudml.org/doc/216495},
volume = {129},
year = {1998},
}

TY - JOUR
AU - Keyantuo, V.
AU - Vieten, P.
TI - On analytic semigroups and cosine functions in Banach spaces
JO - Studia Mathematica
PY - 1998
VL - 129
IS - 2
SP - 137
EP - 156
AB - If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform.
LA - eng
KW - negative square root; holomorphic semigroup; conjugate potential transform of the cosine function
UR - http://eudml.org/doc/216495
ER -

References

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  9. [9] M. Hieber, Integrated semigroups and differential operators on L p ( ℝ N ) -spaces, Math. Ann. 291 (1991), 1-16. 
  10. [10] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ. 31, Amer. Math. Soc. Providence, R.I., 1957. Zbl0078.10004
  11. [11] S. Kurepa, A cosine functional equation in Banach algebras, Acta Sci. Math. (Szeged) 23 (1962), 255-267. Zbl0113.31702
  12. [12] H. R. Thieme, Integrated semigroups and integrated solutions to the abstract Cauchy problem, J. Math. Anal. Appl. 152 (1990), 416-447. Zbl0738.47037
  13. [13] P. Vieten, Holomorphie und Laplace Transformation Banachraumwertiger Funktionen, Ph.D. thesis, Shaker, Aachen, 1995. 
  14. [14] D. V. Widder, An Introduction to Transform Theory, Academic Press, New York, 1971. Zbl0219.44001
  15. [15] K. Yosida, Functional Analysis, Springer, New York, 1980. 

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