A lower bound on the radius of analyticity of a power series in a real Banach space
Timothy Nguyen
Studia Mathematica, Tome 192 (2009), p. 171-179 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Let F be a power series centered at the origin in a real Banach space with radius of uniform convergence ϱ. We show that F is analytic in the open ball B of radius ϱ/√e, and furthermore, the Taylor series of F about any point a ∈ B converges uniformly within every closed ball centered at a contained in B.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:286439 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-2-5,
     author = {Timothy Nguyen},
     title = {A lower bound on the radius of analyticity of a power series in a real Banach space},
     journal = {Studia Mathematica},
     volume = {192},
     year = {2009},
     pages = {171-179},
     zbl = {1193.32001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-2-5}
}

Timothy Nguyen. A lower bound on the radius of analyticity of a power series in a real Banach space. Studia Mathematica, Tome 192 (2009) pp. 171-179. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-2-5/