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 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.

Fourier multipliers on compact groups

1982 ◽  
Vol 94 (1) ◽  
pp. 69-72 ◽  
Author(s):  
T. S. Quek ◽  
Leonard Y. H. Yap
Keyword(s):  
Fourier Multipliers ◽  
Compact Groups

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 Applications of random Fourier series over compact groups to Fourier multipliers

1972 ◽  
Vol 43 (2) ◽  
pp. 531-541 ◽  
Author(s):  
Alessandro Figà-Talamanca ◽  
John Price
Keyword(s):  
Fourier Series ◽  
Fourier Multipliers ◽  
Compact Groups ◽  
Random Fourier Series

scholarly journals Multipliers on spaces of functions on compact groups with p-summable Fourier transforms

1993 ◽  
Vol 47 (3) ◽  
pp. 435-442 ◽  
Author(s):  
Sanjiv Kumar Gupta ◽  
Shobha Madan ◽  
U.B. Tewari
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Fourier Transforms ◽  
Dual Group ◽  
Compact Groups ◽  
Circle Group ◽  
Integrable Functions ◽  
Space Of Integrable Functions

Let G be a compact abelian group with dual group Γ. For 1 ≤ p < ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In particular, we prove that (Ap, Ap) ⊊ (Aq, Aq). For the circle group, we characterise permutation invariant multipliers from Ap to Ar for 1 ≤ r ≤ 2.

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.

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