Power series with integer coefficients in several variables

1987 ◽  
Vol 62 (1) ◽  
pp. 602-615 ◽  
Author(s):  
E. J. Straube
Keyword(s):  
Power Series ◽  
Integer Coefficients ◽  
Several Variables

scholarly journals Some Results of Fekete-Szegö Type. Results for Some Holomorphic Functions of Several Complex Variables

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1707
Author(s):  
Renata Długosz ◽  
Piotr Liczberski
Keyword(s):  
Power Series ◽  
Power Series Expansion ◽  
Holomorphic Functions ◽  
Positive Real Part ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Homogeneous Polynomials ◽  
Positive Real ◽  
Sharp Estimates ◽  
Several Variables

This paper is devoted to a generalization of the well-known Fekete-Szegö type coefficients problem for holomorphic functions of a complex variable onto holomorphic functions of several variables. The considerations concern three families of such functions f, which are bounded, having positive real part and which Temljakov transform Lf has positive real part, respectively. The main result arise some sharp estimates of the Minkowski balance of a combination of 2-homogeneous and the square of 1-homogeneous polynomials occurred in power series expansion of functions from aforementioned families.

scholarly journals Bohr’s power series theorem in several variables

1997 ◽  
Vol 125 (10) ◽  
pp. 2975-2979 ◽  
Author(s):  
Harold P. Boas ◽  
Dmitry Khavinson
Keyword(s):  
Power Series ◽  
Several Variables

A Bernstein–Walsh Type Inequality and Applications

2006 ◽  
Vol 49 (2) ◽  
pp. 256-264 ◽  
Author(s):  
Tejinder Neelon
Keyword(s):  
Power Series ◽  
Type Inequality ◽  
Divergent Series ◽  
Transfinite Diameter ◽  
Several Variables ◽  
Real Analytic ◽  
Positive Capacity ◽  
Double Power Series

AbstractA Bernstein–Walsh type inequality forC∞functions of several variables is derived, which then is applied to obtain analogs and generalizations of the following classical theorems: (1) Bochnak– Siciak theorem: aC∞function on ℝnthat is real analytic on every line is real analytic; (2) Zorn–Lelong theorem: if a double power seriesF(x,y) converges on a set of lines of positive capacity thenF(x,y) is convergent; (3) Abhyankar–Moh–Sathaye theorem: the transfinite diameter of the convergence set of a divergent series is zero.

scholarly journals Some Enumerations on Non-Decreasing Dyck Paths

10.37236/3941 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Éva Czabarka ◽  
Rigoberto Flórez ◽  
Leandro Junes
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Maximum Element ◽  
Dyck Paths ◽  
Several Variables ◽  
Formal Power

We construct a formal power series on several variables that encodes many statistics on non-decreasing Dyck paths. In particular, we use this formal power series to count peaks, pyramid weights, and indexed sums of pyramid weights for all non-decreasing Dyck paths of length $2n.$ We also show that an indexed sum on pyramid weights depends only on the size and maximum element of the indexing set.

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