Multidimensional Analog Modulation and Optimal Mappings

2007 ◽  
Author(s):  
Boris Kravtsov ◽  
Dan Raphaeli
Keyword(s):  
Multidimensional Analog

scholarly journals Four dimensional characterization of bounded double sequences

2004 ◽  
Vol 35 (2) ◽  
pp. 129-134 ◽  
Author(s):  
Richard F. Patterson
Keyword(s):  
Bounded Sequence ◽  
Matrix Transformations ◽  
Double Sequences ◽  
Matrix Methods ◽  
Multidimensional Analog ◽  
Dimensional Matrix ◽  
Important Theorem ◽  
Summability Matrix ◽  
Regular Summability

In 1945 Brudno presented the following important theorem: If $A$ and $B$ are regular summability matrix methods such that every bounded sequence summed by $A$ is also summed by $B$, then it is summed by $B$ to the same value. R. G. Cooke suggested that a simpler proof would be desirable. Petersen presented such a proof. The goal of the paper is to present an accessible multidimensional analog of Brudno theorem for double sequences using four dimensional matrix transformations.

scholarly journals RH-regular transformations which sums a given double sequence

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 625-627 ◽  
Author(s):  
Richard Patterson
Keyword(s):  
Double Sequence ◽  
Divergent Sequence ◽  
Multidimensional Analog

In 1946 P. Erdos and P. C Rosenbloom presented the following theorem that arose out of discussions they had with R. P. Agnew. Let {xn} be a bounded divergent sequence. Suppose that {xn} is summable by every regular Toeplitz method which sums {xn}. Then {yn} is of the form {cxn + an} where {an} is convergent. The goals of the paper includes the presentation of a multidimensional analog of Erdos and Rosenbloom results in [1].

scholarly journals The Multidimensional Analog of the Biberbach Hypothesis for Generalized Star Functions in the Space $\mathbb{C}^{n}$, $n\geq 2$

2017 ◽  
Author(s):  
М.Д. Султыгов
Keyword(s):  
Multidimensional Analog

В статье рассматривается одно из дополнений к фундаментальным результатам геометрической теории многомерного комплексного анализа по проблемам классов голоморфных функций. По радиусам параметризации границ областей Рейнхарта строятся эффективные достаточные условия обобщенно-звездных функций в виде многомерного аналога гипотезы Бибербаха.

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