scholarly journals Orthogonal Expansion of Real Polynomials, Location of Zeros, and an L2 Inequality

2001 ◽  
Vol 109 (1) ◽  
pp. 126-147
Author(s):  
G. Schmeisser
Keyword(s):  
Orthogonal Expansion ◽  
Real Polynomials ◽  
Location Of Zeros

scholarly journals Location of zeros Part I: Real polynomials and entire functions

1983 ◽  
Vol 27 (2) ◽  
pp. 244-278 ◽  
Author(s):  
Thomas Craven ◽  
George Csordas
Keyword(s):  
Entire Functions ◽  
Real Polynomials ◽  
Location Of Zeros

scholarly journals Lee-Yang zeros of the antiferromagnetic Ising model

2021 ◽  
pp. 1-35
Author(s):  
FERENC BENCS ◽  
PJOTR BUYS ◽  
LORENZO GUERINI ◽  
HAN PETERS
Keyword(s):  
Ising Model ◽  
Partition Functions ◽  
Cayley Trees ◽  
Circular Arcs ◽  
Precise Characterization ◽  
Ferromagnetic Ising Model ◽  
Location Of Zeros ◽  
Antiferromagnetic Ising Model ◽  
Recursively Defined Trees ◽  
Degree Bound

Abstract We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the zeros are nowhere dense on the most interesting circular arcs. In contrast, we prove that when considering all graphs with a given degree bound, the zeros are dense in a circular sub-arc, implying that Cayley trees are in this sense not extremal. The proofs rely on describing the rational dynamical systems arising when considering ratios of partition functions on recursively defined trees.

The Location of Zeros

1976 ◽  
pp. 212-251
Author(s):  
George Pólya ◽  
Gabor Szegö
Keyword(s):  
Location Of Zeros

Location of Zeros

2019 ◽  
pp. 81-83
Author(s):  
Vittorino Pata
Keyword(s):  
Location Of Zeros

scholarly journals On realizability of sign patterns by real polynomials

2018 ◽  
Vol 68 (3) ◽  
pp. 853-874 ◽  
Author(s):  
Vladimir Kostov
Keyword(s):  
Real Polynomials ◽  
Sign Patterns

Counting Critical Points of Real Polynomials in Two Variables

1993 ◽  
Vol 100 (3) ◽  
pp. 255 ◽  
Author(s):  
Alan Durfee ◽  
Nathan Kronefeld ◽  
Heidi Munson ◽  
Jeff Roy ◽  
Ina Westby
Keyword(s):  
Critical Points ◽  
Real Polynomials

scholarly journals New Orthogonal Transforms for Signal and Image Processing

2021 ◽  
Vol 11 (16) ◽  
pp. 7433
Author(s):  
Andrzej Dziech
Keyword(s):  
Symmetric Matrix ◽  
Sparse Matrices ◽  
Orthogonal Expansion ◽  
Orthogonal Matrices ◽  
Exponential Form ◽  
Orthogonal Transforms ◽  
Hadamard Transforms ◽  
The Given ◽  
Transform Domains ◽  
Signal Approximation

In the paper, orthogonal transforms based on proposed symmetric, orthogonal matrices are created. These transforms can be considered as generalized Walsh–Hadamard Transforms. The simplicity of calculating the forward and inverse transforms is one of the important features of the presented approach. The conditions for creating symmetric, orthogonal matrices are defined. It is shown that for the selection of the elements of an orthogonal matrix that meets the given conditions, it is necessary to select only a limited number of elements. The general form of the orthogonal, symmetric matrix having an exponential form is also presented. Orthogonal basis functions based on the created matrices can be used for orthogonal expansion leading to signal approximation. An exponential form of orthogonal, sparse matrices with variable parameters is also created. Various versions of orthogonal transforms related to the created full and sparse matrices are proposed. Fast computation of the presented transforms in comparison to fast algorithms of selected orthogonal transforms is discussed. Possible applications for signal approximation and examples of image spectrum in the considered transform domains are presented.

scholarly journals ZEROS OF REAL POLYNOMIALS ON BANACH SPACES

2004 ◽  
Vol 41 (1) ◽  
pp. 77-94
Author(s):  
Jose-G. Llavona
Keyword(s):  
Banach Spaces ◽  
Real Polynomials
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