scholarly journals Some Aspects of Totally Positive Kernels Useful in Information Theory

2019 ◽  
Author(s):  
Semih Yagli ◽  
Alex Dytso ◽  
H. Vincent Poor ◽  
Shlomo Shamai Shitz
Keyword(s):  
Information Theory ◽  
Totally Positive ◽  
Positive Kernels

Convergence of Interpolation to Transforms of Totally Positive Kernels

1988 ◽  
Vol 40 (3) ◽  
pp. 750-768
Author(s):  
N. Dyn ◽  
D. S. Lubinsky
Keyword(s):  
Exponential Sums ◽  
Rational Functions ◽  
Hilbert Transforms ◽  
Convergence Results ◽  
Totally Positive ◽  
Special Cases ◽  
Positive Kernel ◽  
Image Position ◽  
Positive Kernels ◽  
Stieltjes Series

Convergence of exponential sumsthat interpolate to Laplace transforms(1.1)have been studied by several authors [3, 6, 8, 15]. For rational functions that interpolate to Markov functions (also called Hamburger or Stieltjes Series or Hilbert Transforms)(1.2)far more detailed convergence results are available (see [10, 11, 16] and references therein). Both (1.1) and (1.2) are special cases of the transform(1.3)where K(x, t) is a strictly totally positive kernel.

A theorem on order relations generated by totally positive kernels

1995 ◽  
Vol 186 (9) ◽  
pp. 1241-1269 ◽  
Author(s):  
M L Gerver ◽  
E A Kudryavtseva
Keyword(s):  
Order Relations ◽  
Totally Positive ◽  
Positive Kernels
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