Discrete analogs of inequalities of Wirtinger

1955 ◽  
Vol 59 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Ky Fan ◽  
Olga Taussky ◽  
John Todd
Keyword(s):  
Discrete Analogs

scholarly journals Algebraic methods in discrete analogs of the Kakeya problem

2010 ◽  
Vol 225 (5) ◽  
pp. 2828-2839 ◽  
Author(s):  
Larry Guth ◽  
Nets Hawk Katz
Keyword(s):  
Algebraic Methods ◽  
Kakeya Problem ◽  
Discrete Analogs

Convergence and applications of reproducing kernels for classes of discrete harmonic functions

1974 ◽  
Vol 11 (3) ◽  
pp. 339-358
Author(s):  
C. Wayne Mastin
Keyword(s):  
Harmonic Functions ◽  
Reproducing Kernels ◽  
Biharmonic Operator ◽  
Convergence Properties ◽  
Interpolation Problems ◽  
Discrete Analogs ◽  
Discrete Harmonic Functions

This paper gives convergence properties and applications of the discrete analogs of reproducing kernels for various families of harmonic functions. From these results information is obtained on the solution of interpolation problems, the convergence of the discrete Neumann's function, and the solution to problems involving the discrete biharmonic operator.

scholarly journals The formulas for sum of products of sequences associated with the metallic means

2020 ◽  
Vol 1 (1) ◽  
pp. 73-78
Author(s):  
P. Kosobutskyy ◽  
N. Nestor
Keyword(s):  
Signal Processing ◽  
Closed Form ◽  
Fibonacci Numbers ◽  
Statistical Signal Processing ◽  
Discrete Data ◽  
Definite Integrals ◽  
Sum Of Products ◽  
Finite Sums ◽  
Discrete Analogs

In this paper, the regularities of convolution of sequences c of Fibonacci numbers {Fn} generated by metallic means and the sum of products of two statistically independent sequences {Fi} and Jn=j∙sin(0.5π(n-j)) are investigated. It is shown that the known closed forms of sums for convolution and product are similar. Attention to the study of the convolution of two sequences of discrete data is associated with the use of this method for statistical signal processing. This problem involves calculating finite sums as discrete analogs of definite integrals. Such a problem is considered solved if the formula for the sum is expressed in a closed form as a function of its members and their number.

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