# A note on a formula for the fractional powers of infinitesimal generators of semigroups

Studia Mathematica (1996)

- Volume: 119, Issue: 3, page 247-254
- ISSN: 0039-3223

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topMartinez, Celso, and Sanz, Miguel. "A note on a formula for the fractional powers of infinitesimal generators of semigroups." Studia Mathematica 119.3 (1996): 247-254. <http://eudml.org/doc/216298>.

@article{Martinez1996,

abstract = {If -A is the generator of an equibounded $C_0$-semigroup and 0 < Re α < m (m integer), its fractional power $A^α$ can be described in terms of the semigroup, through a formula that is only valid if a certain function $K_\{α,m\}$ is nonzero. This paper is devoted to the study of the zeros of $K_\{α,m\}$.},

author = {Martinez, Celso, Sanz, Miguel},

journal = {Studia Mathematica},

keywords = {generator of an equibounded -semigroup; fractional power},

language = {eng},

number = {3},

pages = {247-254},

title = {A note on a formula for the fractional powers of infinitesimal generators of semigroups},

url = {http://eudml.org/doc/216298},

volume = {119},

year = {1996},

}

TY - JOUR

AU - Martinez, Celso

AU - Sanz, Miguel

TI - A note on a formula for the fractional powers of infinitesimal generators of semigroups

JO - Studia Mathematica

PY - 1996

VL - 119

IS - 3

SP - 247

EP - 254

AB - If -A is the generator of an equibounded $C_0$-semigroup and 0 < Re α < m (m integer), its fractional power $A^α$ can be described in terms of the semigroup, through a formula that is only valid if a certain function $K_{α,m}$ is nonzero. This paper is devoted to the study of the zeros of $K_{α,m}$.

LA - eng

KW - generator of an equibounded -semigroup; fractional power

UR - http://eudml.org/doc/216298

ER -

## References

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- [7] J. L. Lions et J. Peetre, Sur une classe d'espaces d'interpolation, Publ. Math. Inst. Hautes Etudes Sci. 19 (1964), 5-68.
- [8] C. Martinez and M. Sanz, Fractional powers of non-densely defined operators, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 18 (1991), 443-454. Zbl0811.47013
- [9] C. Martinez, M. Sanz and L. Marco, Fractional powers of operators, J. Math. Soc. Japan 40 (1988), 331-347. Zbl0628.47006
- [10] J. D. Stafney, Integral representations of fractional powers of infinitesimal generators, Illinois J. Math. 20 (1976), 124-133. Zbl0315.47025
- [11] U. Westphal, An approach to fractional powers of operators via fractional differences, Proc. London Math. Soc. (3) 29 (1974), 557-576. Zbl0294.47030

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