Bohr’s Theorem for Monogenic Power Series
نویسندگان
چکیده
The main goal of this paper is to generalize Bohr’s phenomenon from complex one-dimensional analysis to higher dimensions in the framework of Quaternionic Analysis. MSC 2000: 30G35
منابع مشابه
Bohr’s Power Series Theorem in Several Variables
Generalizing a classical one-variable theorem of Bohr, we show that if an n-variable power series has modulus less than 1 in the unit polydisc, then the sum of the moduli of the terms is less than 1 in the polydisc of radius 1/(3 √ n ). How large can the sum of the moduli of the terms of a convergent power series be? Harald Bohr addressed this question in 1914 with the following remarkable resu...
متن کامل2 1 A pr 1 99 8 Multidimensional analogues of Bohr ’ s theorem on power series ∗
Generalizing the classical result of Bohr, we show that if an nvariable power series converges in an n-circular bounded complete domain D and its sum has modulus less than 1, then the sum of the maximum of the moduli of the terms is less than 1 in the homothetic domain r · D, where r = 1 − n √ 2/3. This constant is near to the best one for the domain D = {z : |z1| + . . . + |zn| < 1}. 1 Prelimi...
متن کاملComments on Multiparameter Estimation in Truncated Power Series Distributions under the Stein's Loss
This comment is to show that Theorem3.3 of Dey and Chung (1991) (Multiparameter estimation intruncated power series distributions under the Stein's loss.emph{Commun. Statist.-Theory Meth.,} {bf 20}, 309-326) may giveus misleading results. Analytically and through simulation, weshow that the Theorem does not improve the given estimator.
متن کاملRemarks on the Bohr Phenomenon
Bohr’s theorem ([10]) states that analytic functions bounded by 1 in the unit disk have power series ∑ anz n such that ∑ |an||z| < 1 in the disk of radius 1/3 (the so-called Bohr radius.) On the other hand, it is known that there is no such Bohr phenomenon in Hardy spaces with the usual norm, although it is possible to build equivalent norms for which a Bohr phenomenon does occur! In this paper...
متن کاملSlice monogenic functions
In this paper we offer a new definition of monogenicity for functions defined on R with values in the Clifford algebra Rn following an idea inspired by the recent papers [6], [7]. This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the Clifford algebra Rn. We will prove a Cauchy integral formula as well as some of its conseque...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008