scholarly journals Wavelet subspaces invariant under groups of translation operators

2003 ◽  
Vol 113 (2) ◽  
pp. 171-178
Author(s):  
Biswaranjan Behera ◽  
Shobha Madan
Keyword(s):  
Translation Operators ◽  
Wavelet Subspaces

Diagonalization of Translation Operators for Elastic Wave Equations

PIERS Online ◽  
2008 ◽  
Vol 4 (2) ◽  
pp. 271-275
Author(s):  
Bo He ◽  
Weng Cho Chew
Keyword(s):  
Elastic Wave ◽  
Wave Equations ◽  
Elastic Wave Equations ◽  
Translation Operators

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

scholarly journals Converting translation operators into plane polar and spherical coordinates and their use in determining quantum-mechanical wavefunctions in a representation-independent fashion

2021 ◽  
Vol 62 (7) ◽  
pp. 072102
Author(s):  
Michael Rushka ◽  
M. A. Esrick ◽  
W. N. Mathews ◽  
J. K. Freericks
Keyword(s):  
Quantum Mechanical ◽  
Spherical Coordinates ◽  
Translation Operators

A new version of the Fast Multipole Method for the Laplace equation in three dimensions

Acta Numerica ◽  
1997 ◽  
Vol 6 ◽  
pp. 229-269 ◽  
Author(s):  
Leslie Greengard ◽  
Vladimir Rokhlin
Keyword(s):  
Laplace Equation ◽  
Fast Multipole Method ◽  
High Accuracy ◽  
Three Dimensions ◽  
Potential Fields ◽  
Diagonal Form ◽  
Fast Multipole ◽  
Reasonable Cost ◽  
Multipole Method ◽  
Translation Operators

We introduce a new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions. It is based on a new diagonal form for translation operators and yields high accuracy at a reasonable cost.

Weighted translation operators generated by mappings with saddle points: a model class

2010 ◽  
Vol 164 (4) ◽  
pp. 497-517 ◽  
Author(s):  
A. B. Antonevich ◽  
Yu. Yakubovska
Keyword(s):  
Saddle Points ◽  
Translation Operators ◽  
Model Class ◽  
Weighted Translation

A sampling theorem for wavelet subspaces

1992 ◽  
Vol 38 (2) ◽  
pp. 881-884 ◽  
Author(s):  
G.G. Walter
Keyword(s):  
Sampling Theorem ◽  
Wavelet Subspaces

Generalized average sampling and reconstruction for wavelet subspaces

2018 ◽  
Vol 26 (2) ◽  
pp. 333-342
Author(s):  
S. Yugesh ◽  
P. Devaraj
Keyword(s):  
Average Sampling ◽  
Wavelet Subspaces ◽  
Sampling And Reconstruction

scholarly journals Hybrid multilevel plane wave based near-field far-field transformation utilising combined near- and far-field translations

2009 ◽  
Vol 7 ◽  
pp. 17-22 ◽  
Author(s):  
C. H. Schmidt ◽  
T. F. Eibert
Keyword(s):  
Near Field ◽  
Measurement Techniques ◽  
Plane Waves ◽  
Low Complexity ◽  
Far Field ◽  
Computation Complexity ◽  
Low Frequencies ◽  
Field Transformation ◽  
Translation Operators ◽  
Equivalent Sources

Abstract. The radiation of large antennas and those operating at low frequencies can be determined efficiently by near-field measurement techniques and a subsequent near-field far-field transformation. Various approaches and algorithms have been researched but for electrically large antennas and irregular measurement contours advanced algorithms with low computation complexity are required. In this paper an algorithm employing plane waves as equivalent sources and utilising efficient diagonal translation operators is presented. The efficiency is further enhanced using simple far-field translations in combination with the expensive near-field translations. In this way a low complexity near-field transformation is achieved, which works for arbitrary sample point distributions and incorporates a full probe correction without increasing the complexity.

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