Compressed sensing from a harmonic analysis point of view

2016 ◽  
Vol 42 (1) ◽  
pp. 19-29
Author(s):  
J. -P. Kahane
Keyword(s):  
Compressed Sensing ◽  
Harmonic Analysis ◽  
Point Of View ◽  
Analysis Point

scholarly journals Questions Around the Thue-Morse Sequence

2018 ◽  
Vol 13 (1) ◽  
pp. 1-25
Author(s):  
Martine Queffélec
Keyword(s):  
Harmonic Analysis ◽  
Point Of View ◽  
Open Questions ◽  
Analysis Point

Abstract We intend to unroll the surprizing properties of the Thue-Morse sequence with a harmonic analysis point of view, and mention in passing some related open questions.

scholarly journals HURWITZ THEOREM AND PARALLELIZABLE SPHERES FROM TENSOR ANALYSIS

2001 ◽  
Vol 16 (25) ◽  
pp. 4207-4222 ◽  
Author(s):  
J. A. NIETO ◽  
L. N. ALEJO-ARMENTA
Keyword(s):  
Clifford Algebra ◽  
Point Of View ◽  
Tensor Analysis ◽  
Tensor Algebra ◽  
Normed Algebra ◽  
Curved Spaces ◽  
Hurwitz Theorem ◽  
Analysis Point

By using tensor analysis, we find a connection between normed algebras and the parallelizability of the spheres S 1, S 3 and S 7. In this process, we discovered the analog of Hurwitz theorem for curved spaces and a geometrical unified formalism for the metric and the torsion. In order to achieve these goals we first develop a proof of Hurwitz theorem based on tensor analysis. It turns out that in contrast to the doubling procedure and Clifford algebra mechanism, our proof is entirely based on tensor algebra applied to the normed algebra condition. From the tersor analysis point of view our proof is straightforward and short. We also discuss a possible connection between our formalism and the Cayley–Dickson algebras and Hopf maps.

scholarly journals Effects of N, P, K and S application on yield and quality of white jute (Corchorus capsularis L.) var. BJC-2197

2012 ◽  
Vol 21 (2) ◽  
pp. 109-116
Author(s):  
Sayma Khanom ◽  
Sonia Hosssain ◽  
Shahid Akhtar Hossain
Keyword(s):  
Growth Yield ◽  
Quality Parameters ◽  
Point Of View ◽  
Corchorus Capsularis ◽  
Yield And Quality ◽  
S Application ◽  
Positive Effect ◽  
S Fertilizers ◽  
Analysis Point

A field experiment was conducted at Bangladesh Jute Research Institute (BJRI) to observe the response of N, P, K and S on a pre?released white jute (Corchorus capsularis) var. BJC?2197. The experiment was carried out by applying N, P, K, S fertilizers in ten combinations including control. From the experiment it was observed that all the treatments had significant positive effect over control on growth, yield and quality parameters. The highest fiber yield (3.21 t/ha) and stick yield (6.58 t/ha) were recorded with N90P5K30S10 kg/ha treatment. However, the best quality fiber was found with combination of N90P15K30S10 kg/ha treatment. From the economic analysis point of view, it was found that combination of N90P5K30S10 kg/ha was higher (2.30) than N90P15K30S10 kg/ha (2.04). So the former can be considered as the best combination for var. BJC?2197 in terms of BCR, yield and quality. Dhaka Univ. J. Biol. Sci. 21(2): 109?116, 2012 (July) DOI: http://dx.doi.org/10.3329/dujbs.v21i2.11508

scholarly journals IX. On the application of harmonic analysis to the dynamical theory of the tides. — Part I. On laplace’s "oscillations of the first species” and the dynamics of ocean currents

1897 ◽  
Vol 189 ◽  
pp. 201-257 ◽  
Keyword(s):  
Ab Initio ◽  
Harmonic Analysis ◽  
Dynamical Theory ◽  
Point Of View ◽  
Ocean Currents ◽  
Long Period ◽  
Dynamical Treatment ◽  
The Subject ◽  
Hydrodynamical Theory

The earliest attempt to subject the Theory of the Tides to a rigorous dynamical treatment was given by Laplace in the first and fourth books of the ‘Mécanique Céleste.’ The subject has since been treated by Airy, Kelvin, Darwin, Lamb, and other writers, but with the exception of the extension of Laplace’s results to include the theory of the long-period tides, but little practical advance has been made with the subject, in spite of the enormous increase in the power of the mathematical resources at our disposal, and the problem has remained in very much the same condition as it was left by Laplace. This arises no doubt partly from the difficulties inherent to the subject, but partly from the form in which the theory was originally presented by Laplace in the ‘Mécanique Céleste,’ which has been described by Airy as “perhaps on the whole more obscure than any other part of the same extent in that work.” The obscurity complained of does not however seem to have been entirely removed by Laplace’s successors, and it was the fact that every presentment of the theory with which I was acquainted offered some points of difficulty, that in the first instance led me to take up the problem ab initio , partly with the purpose of allaying the doubts which had arisen in my own mind as to the validity of certain approximations employed by Laplace and adopted by his successors, and partly in the hope that I might be able to extend the results of Laplace to meet more fully the case presented by the circumstances actually existent in Nature. Up to the present I have been unable to free the problem to any extent from the limitations which have been imposed by previous writers, and consequently it would be futile to claim that the results I am now able to put forward materially advance our knowledge of the tides as they actually exist; but I venture to hope that these results, as applied to the oscillations of an ideal ocean, considerably simpler in character than the actual ocean, may prove of some interest from the point of view of pure hydrodynamical theory.

Degenerate curves and harmonic analysis

1990 ◽  
Vol 108 (1) ◽  
pp. 89-96 ◽  
Author(s):  
S. W. Drury
Keyword(s):  
Harmonic Analysis ◽  
Correct Choice ◽  
Degenerate Case ◽  
Point Of View ◽  
Affine Geometry ◽  
The Poor ◽  
Reference Measure ◽  
Affine Arclength

This article deals with several related questions in harmonic analysis which are well understood for non-degenerate curves in ℝn, but poorly understood in the degenerate case. These questions invariably involve a positive ‘reference’ measure on the curve. In the non-degenerate case the choice of measure is not particularly critical and it is usually taken to be the Euclidean arclength measure. Since the questions considered here are invariant under the group of affine motions (of determinant 1), the correct choice of reference measure is the affine arclength measure. We refer the reader to Guggenheimer [8] for information on affine geometry. When the curve has degeneracies, the choice of measure becomes critical and it is the affine arclength measure which yields the most powerful results. From the Euclidean point of view the affine arclength measure has correspondingly little mass near the degeneracies and thus compensates automatically for the poor behaviour there. This principle should also be valid for general submanifolds of ℝn but alas the affine geometry of submanifolds is itself not well understood in general.

First harmonic analysis: a circuit theory point of view

1999 ◽  
Vol 42 (1) ◽  
pp. 65-71 ◽  
Author(s):  
I. Sebastiao Bonatti ◽  
P.L. Dias Peres ◽  
J. Antenor Pomilio
Keyword(s):  
Harmonic Analysis ◽  
Circuit Theory ◽  
Point Of View ◽  
Theory Point

scholarly journals Anisotropic random walks on free products of cyclic groups, irreducible representations and idempotents of C*reg(G)

1992 ◽  
Vol 128 ◽  
pp. 95-120 ◽  
Author(s):  
Gabriella Kuhn
Keyword(s):  
Harmonic Analysis ◽  
Homogeneous Space ◽  
Free Product ◽  
Dual Space ◽  
Von Neumann Algebra ◽  
Point Of View ◽  
Irreducible Representations ◽  
Free Products ◽  
Von Neumann ◽  
Cyclic Groups

Let be the free product of q + 1 copies of Zn+1 and let denote its Cayley graph (with respect to aj, 1 ≤ j ≤ q + 1). We may think of G as a group acting on the “homogeneous space” , This point of view is inspired by the case of SL2(R) acting on the hyperbolic disk and is developed in [FT-P] [I-P] [FT-S] [S] (but see also [C]).Since G is a group we may investigate some classical topics: the full (reductive) C* algebra, its dual space, the regular Von Neumann algebra and so on. See [B] [P] [L] [V] and also [H]. These approaches give results pointing up the analogy between harmonic analysis on these groups and harmonic analysis on more classical objects.

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