scholarly journals Titchmarsh theorems for Fourier transforms of Hölder–Lipschitz functions on compact homogeneous manifolds

2019 ◽  
Vol 189 (1) ◽  
pp. 23-49 ◽  
Author(s):  
Radouan Daher ◽  
Julio Delgado ◽  
Michael Ruzhansky
Keyword(s):  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Homogeneous Manifolds

scholarly journals Fourier transforms of Lipschitz functions on the hyperbolic planeH2

1998 ◽  
Vol 21 (2) ◽  
pp. 397-401 ◽  
Author(s):  
M. S. Younis
Keyword(s):  
Hyperbolic Plane ◽  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Order Of Magnitude ◽  
Complex Valued ◽  
Lipschitz Conditions

The purpose of the present work is to study the order of magnitude of the Fourier transformsfˆ(λ)for largeλof complex-valued functionsf(z)sating certain Lipschitz conditions in the non-Euclidean hyperbolic planeH2.

scholarly journals Fourier transforms of Dini-Lipschitz functions

1986 ◽  
Vol 9 (2) ◽  
pp. 301-312 ◽  
Author(s):  
M. S. Younis
Keyword(s):  
Fourier Series ◽  
Dual Space ◽  
Fourier Coefficients ◽  
Absolute Convergence ◽  
Fourier Transforms ◽  
Function Class ◽  
Lipschitz Functions ◽  
Lipschitz Class ◽  
The Absolute ◽  
Lipschitz Conditions

It is well known that if Lipschitz conditions of a certain order are imposed on a functionf(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms off. In general, iff(x)belongs to a certain function class, then the Lipschitz conditions have bearing as to the dual space to which the Fourier coefficients and transforms off(x)belong. In the present work we do study the same phenomena for the wider Dini-Lipschitz class as well as for some other allied classes of functions.

scholarly journals The Fourier transforms of Lipschitz functions on certain domains

1997 ◽  
Vol 20 (4) ◽  
pp. 817-822 ◽  
Author(s):  
M. S. Younis
Keyword(s):  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Motion Group ◽  
Hankel Transforms

The Fourier transforms of certain Lipschitz functions are discussed and compared with the Hankel transforms of these functions and with their Fourier transforms on the Euclidean Cartan Motion groupM(n),n≥2.

scholarly journals Fourier transforms of Dini-Lipschitz functions on Vilenkin groups

1992 ◽  
Vol 15 (3) ◽  
pp. 609-612
Author(s):  
M. S. Younis
Keyword(s):  
Fourier Series ◽  
Euclidean Space ◽  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Dimensional Euclidean Space ◽  
Vilenkin Groups ◽  
Lipschitz Conditions

In [4] we proved some theorems on the Fourier Transforms of functions satisfying conditions related to the Dini-Lipschitz conditions on then-dimensional Euclidean spaceRnand the torus groupTn. In this paper we extend those theorems for functions with Fourier series on Vilenkin groups.

scholarly journals The Fourier transforms of Lipschitz functions on the Heisenberg group

2000 ◽  
Vol 24 (1) ◽  
pp. 5-9 ◽  
Author(s):  
M. S. Younis
Keyword(s):  
Heisenberg Group ◽  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Order Of Magnitude

We study the order of magnitude of the Fourier transforms of certain Lipschitz functions on the Heisenberg groupHn. We compare our conclusions with some previous results in the field.

Fourier transforms of lipschitz functions and fourier multipliers on compact groups

1983 ◽  
Vol 182 (4) ◽  
pp. 537-548 ◽  
Author(s):  
Tong-Seng Quek ◽  
Leonard Y. H. Yap
Keyword(s):  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Fourier Multipliers ◽  
Compact Groups

scholarly journals Fourier transforms of Lipschitz functions on certain Lie groups

2001 ◽  
Vol 27 (7) ◽  
pp. 439-448 ◽  
Author(s):  
M. S. Younis
Keyword(s):  
Lie Groups ◽  
Linear Group ◽  
Fourier Transforms ◽  
Special Linear Group ◽  
Lipschitz Functions ◽  
Special Linear ◽  
Order Of Magnitude ◽  
Real Matrices

We study the order of magnitude of the Fourier transforms of certain Lipschitz functions on the special linear group of real matrices of order two.

Fourier Transforms of Dini–Lipschitz Functions on Rank 1 Symmetric Spaces

2016 ◽  
Vol 13 (6) ◽  
pp. 4401-4411 ◽  
Author(s):  
S. Fahlaoui ◽  
M. Boujeddaine ◽  
M. El Kassimi
Keyword(s):  
Symmetric Spaces ◽  
Fourier Transforms ◽  
Lipschitz Functions

Computer processing of high-resolution images of periodic specimens

1986 ◽  
Vol 44 ◽  
pp. 2-5
Author(s):  
W. Chiu ◽  
M.F. Schmid ◽  
T.-W. Jeng
Keyword(s):  
High Resolution ◽  
Fourier Transforms ◽  
Complex Structure ◽  
Distribution Functions ◽  
Multiple Image ◽  
Cryo Electron Microscopy ◽  
Structure Factors ◽  
Unit Cells ◽  
High Resolution Images ◽  
Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

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