Bohr property of bases in the space of entire functions and its generalizations
Aytuna, Aydın and Djakov, Plamen Borissov (2013) Bohr property of bases in the space of entire functions and its generalizations. Bulletin of the London Mathematical Society, 45 (2). pp. 411-420. ISSN 0024-6093 (Print) 1469-2120 (Online)
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Official URL: http://dx.doi.org/10.1112/blms/bds120
We prove that if (phi(n))(n=0)(infinity), phi(0) equivalent to 1, is a basis in the space of entire functions of d complex variables, d >= 1, then, for every compact K subset of C-d, there is a compact K-1 superset of K such that, for every entire function f = Sigma(infinity)(n=0) f(n)phi(n), we have Sigma(infinity)(n=0) vertical bar f(n)vertical bar sup(K) vertical bar phi(n)vertical bar <= sup(K1) vertical bar f vertical bar. A similar assertion holds for bases in the space of global analytic functions on a Stein manifold with the Liouville Property.
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