Harmonic Analysis in Euclidean Space

1998 ◽  
pp. 123-157
Author(s):  
Jayakumar Ramanathan
Keyword(s):  
Euclidean Space ◽  
Harmonic Analysis

scholarly journals On Euclidean Designs and Potential Energy

10.37236/8 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Tsuyoshi Miezaki ◽  
Makoto Tagami
Keyword(s):  
Linear Programming ◽  
Lower Bound ◽  
Euclidean Space ◽  
Potential Energy ◽  
Harmonic Analysis ◽  
Upper Bound ◽  
Type Inequality ◽  
Linear Programming Bound ◽  
Concentric Spheres ◽  
Finite Set

We study Euclidean designs from the viewpoint of the potential energy. For a finite set in Euclidean space, we formulate a linear programming bound for the potential energy by applying harmonic analysis on a sphere. We also introduce the concept of strong Euclidean designs from the viewpoint of the linear programming bound, and we give a Fisher type inequality for strong Euclidean designs. A finite set on Euclidean space is called a Euclidean $a$-code if any distinct two points in the set are separated at least by $a$. As a corollary of the linear programming bound, we give a method to determine an upper bound on the cardinalities of Euclidean $a$-codes on concentric spheres of given radii. Similarly we also give a method to determine a lower bound on the cardinalities of Euclidean $t$-designs as an analogue of the linear programming bound.

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products

Classical and Multilinear Harmonic Analysis

2009 ◽  
Author(s):  
Camil Muscalu ◽  
Wilhelm Schlag
Keyword(s):  
Harmonic Analysis
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