# On analytic semigroups and cosine functions in Banach spaces

Studia Mathematica (1998)

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

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topKeyantuo, 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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