scholarly journals Discrete Fourier analysis with lattices on planar domains

2010 ◽  
Vol 55 (2-3) ◽  
pp. 279-300 ◽  
Author(s):  
Huiyuan Li ◽  
Jiachang Sun ◽  
Yuan Xu
Keyword(s):  
Fourier Analysis ◽  
Discrete Fourier Analysis ◽  
Planar Domains

Discrete Fourier Analysis for Quotient Multipliers

1979 ◽  
Vol 93 (1) ◽  
pp. 233-238 ◽  
Author(s):  
Árpád Száz
Keyword(s):  
Fourier Analysis ◽  
Discrete Fourier Analysis

Moire-based corneal topographer suitable for discrete Fourier analysis

1994 ◽  
Author(s):  
Franciscus H. M. Jongsma ◽  
Fons C. Laan ◽  
Bertho A. T. Stultiens
Keyword(s):  
Fourier Analysis ◽  
Discrete Fourier Analysis

Intersecting Families are Essentially Contained in Juntas

2009 ◽  
Vol 18 (1-2) ◽  
pp. 107-122 ◽  
Author(s):  
IRIT DINUR ◽  
EHUD FRIEDGUT
Keyword(s):  
Fourier Analysis ◽  
Boolean Functions ◽  
Simple Description ◽  
Discrete Fourier Analysis ◽  
Intersecting Family ◽  
Intersecting Families ◽  
Positive Integers

A family$\J$of subsets of {1, . . .,n} is called aj-junta if there existsJ⊆ {1, . . .,n}, with |J| =j, such that the membership of a setSin$\J$depends only onS∩J.In this paper we provide a simple description of intersecting families of sets. Letnandkbe positive integers withk<n/2, and let$\A$be a family of pairwise intersecting subsets of {1, . . .,n}, all of sizek. We show that such a family is essentially contained in aj-junta$\J$, wherejdoes not depend onnbut only on the ratiok/nand on the interpretation of ‘essentially’.Whenk=o(n) we prove that every intersecting family ofk-sets is almost contained in a dictatorship, a 1-junta (which by the Erdős–Ko–Rado theorem is a maximal intersecting family): for any such intersecting family$\A$there exists an elementi∈ {1, . . .,n} such that the number of sets in$\A$that do not containiis of order$\C {n-2}{k-2}$(which is approximately$\frac {k}{n-k}$times the size of a maximal intersecting family).Our methods combine traditional combinatorics with results stemming from the theory of Boolean functions and discrete Fourier analysis.

scholarly journals A discrete Fourier analysis of coarse mesh rebalancing and some associated iterative methods

1983 ◽  
Vol 25 (2) ◽  
pp. 190-216 ◽  
Author(s):  
J. M. Barry ◽  
J. H. Jenkinson ◽  
J. P. Pollard
Keyword(s):  
Fourier Analysis ◽  
Iterative Methods ◽  
Local Mode ◽  
Test Problems ◽  
Relaxation Techniques ◽  
Potential Candidate ◽  
Coarse Mesh ◽  
Relaxation Methods ◽  
Global Mode ◽  
Discrete Fourier Analysis

AbstractIterative methods for solving systems of linear equations may be accelerated by coarse mesh rebalance techniques. The iterative technique, the Method of Implicit Non-stationary Iteration (MINI), is examined through a local-mode Fourier analysis and compared to relaxation techniques as a potential candidate for such acceleration. Results of a global-mode Fourier analysis for MINI, relaxation methods, and the conjugate gradient method are reported for two test problems.

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