scholarly journals The Relationship Between ϵ-Kronecker Sets and Sidon Sets

2016 ◽  
Vol 59 (3) ◽  
pp. 521-527 ◽  
Author(s):  
Kathryn Hare ◽  
L. Thomas Ramsey
Keyword(s):  
Fourier Transform ◽  
Abelian Group ◽  
Dual Group ◽  
Sidon Sets ◽  
Sidon Set ◽  
Arithmetic Properties ◽  
The Fourier Transform ◽  
The Relationship ◽  
Discrete Abelian Group

AbstractA subset E of a discrete abelian group is called ϵ-Kronecker if all E-functions of modulus one can be approximated to within ϵ by characters. E is called a Sidon set if all bounded E-functions can be interpolated by the Fourier transform of measures on the dual group. As ϵ-Kronecker sets with ϵ < 2 possess the same arithmetic properties as Sidon sets, it is natural to ask if they are Sidon. We use the Pisier net characterization of Sidonicity to prove this is true.

scholarly journals Multipliers from spaces of test functions to amalgams

1993 ◽  
Vol 54 (1) ◽  
pp. 97-110
Author(s):  
Maria Torres De Squire
Keyword(s):  
Fourier Transform ◽  
Abelian Group ◽  
Compact Abelian Group ◽  
Continuous Functions ◽  
Locally Compact Abelian Group ◽  
Test Functions ◽  
Space Of Continuous Functions ◽  
Locally Compact ◽  
The Fourier Transform

AbstractIn this paper we study the space of multipliers M(r, s: p, q) from the space of test functions Φrs(G), on a locally compact abelian group G, to amalgams (Lp, lq)(G); the former includes (when r = s = ∞) the space of continuous functions with compact support and the latter are extensions of the Lp(G) spaces. We prove that the space M(∞: p) is equal to the derived space (Lp)0 defined by Figá-Talamanca and give a characterization of the Fourier transform for amalgams in terms of these spaces of multipliers.

scholarly journals HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
Gaussian Distributions ◽  
Discrete Abelian Group

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

scholarly journals The algebra of functions with Fourier transforms in a given function space

1973 ◽  
Vol 9 (1) ◽  
pp. 73-82 ◽  
Author(s):  
U.B. Tewari ◽  
A.K. Gupta
Keyword(s):  
Fourier Transform ◽  
Abelian Group ◽  
Function Space ◽  
Compact Abelian Group ◽  
Fourier Transforms ◽  
Dual Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Algebra Of Functions

Let G be a locally compact abelian group and Ĝ be its dual group. For 1 ≤ p < ∞, let Ap (G) denote the set of all those functions in L1(G) whose Fourier transforms belong to Lp (Ĝ). Let M(Ap (G)) denote the set of all functions φ belonging to L∞(Ĝ) such that is Fourier transform of an L1-function on G whenever f belongs to Ap (G). For 1 ≤ p < q < ∞, we prove that Ap (G) Aq(G) provided G is nondiscrete. As an application of this result we prove that if G is an infinite compact abelian group and 1 ≤ p ≤ 4 then lp (Ĝ) M(Ap(G)), and if p > 4 then there exists ψ є lp (Ĝ) such that ψ does not belong to M(Ap (G)).

Computers and infrared spectroscopy: evolution and revolution

1991 ◽  
Vol 69 (11) ◽  
pp. 1781-1785 ◽  
Author(s):  
D. J. Moffatt ◽  
J. K. Kauppinen ◽  
H. H. Mantsch
Keyword(s):  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Key Words ◽  
Maximum Entropy ◽  
Input Data ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
History Of ◽  
The Fourier Transform ◽  
The Relationship

A brief history of the relationship between computer and infrared spectroscopist is given with emphasis on the use of the Fourier transform. Subsequently, an algorithm is developed that may be used to devise an objective Fourier self-deconvolution procedure which depends only on the input data and is not subject to the biases that are often introduced in such subjective techniques. Key words: deconvolution, Fourier transform, maximum entropy method.

Pego everywhere

2016 ◽  
Vol 15 (04) ◽  
pp. 1650074 ◽  
Author(s):  
Przemysław Górka ◽  
Tomasz Kostrzewa
Keyword(s):  
Fourier Transform ◽  
Abelian Groups ◽  
General Version ◽  
Pontryagin Duality ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups ◽  
The Fourier Transform ◽  
Compact Subsets

In this note we show the general version of Pego’s theorem on locally compact abelian groups. The proof relies on the Pontryagin duality as well as on the Arzela–Ascoli theorem. As a byproduct, we get the characterization of relatively compact subsets of [Formula: see text] in terms of the Fourier transform.

Sets of zero discrete harmonic density

2009 ◽  
Vol 148 (2) ◽  
pp. 253-266 ◽  
Author(s):  
COLIN C. GRAHAM ◽  
KATHRYN E. HARE
Keyword(s):  
Abelian Group ◽  
Dual Group ◽  
New Approach ◽  
Sidon Sets ◽  
Harmonic Density

AbstractLet G be a compact, connected, abelian group with dual group Γ. The set E ⊂ has zero discrete harmonic density (z.d.h.d.) if for every open U ⊂ G and μ ∈ Md(G) there exists ν ∈ Md(U) with = on E. I0 sets in the duals of these groups have z.d.h.d. We give properties of such sets, exhibit non-Sidon sets having z.d.h.d., and prove union theorems. In particular, we prove that unions of I0 sets have z.d.h.d. and provide a new approach to two long-standing problems involving Sidon sets.

Preparation and Characterization of Heparin-Immobilized Poly(Ether Urethanes)

2011 ◽  
Vol 393-395 ◽  
pp. 236-239
Author(s):  
Li Ming Lian ◽  
Bing Leng ◽  
Xiao Hua Ma
Keyword(s):  
Contact Angle ◽  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Aqueous Solutions ◽  
Fourier Transform Infrared Spectroscopy ◽  
Toluidine Blue ◽  
Water Contact ◽  
The Fourier Transform ◽  
Hydrolysis Of

Heparin (Hep)-immobilized poly(ether urethanes) (PU) was prepared by a unique preparation procedure. Firstly, the poly(ether urethanes)(PU) containing diester groups in the side chains were synthesized. Then, PU was dispersed in aqueous solutions and immobilized with heparin after the hydrolysis of diester groups and carboxylation. The Fourier transform infrared spectroscopy (FTIR) and water contact angle (WCA) were used to characterize the heparin-bonded PU. The amount of heparin grafted on the PU was determined to be 0.57wt.% by the toluidine blue method. The heparin-immobilized PU could release just 12% of the immobilized heparin in the early 10 hours of the 70 hours immobilized heparin stability test.

scholarly journals Temperature-Dependent Broadening of the Ultraviolet Photoelectron Spectrum of Au(110)

Sensors ◽  
2021 ◽  
Vol 21 (17) ◽  
pp. 5969
Author(s):  
Tomonari Nishida ◽  
Ikuo Kinoshita ◽  
Juntaro Ishii
Keyword(s):  
Fourier Transform ◽  
Temperature Dependence ◽  
Photoelectron Spectroscopy ◽  
Photoelectron Spectrum ◽  
Thermodynamic Temperature ◽  
Temperature Dependent ◽  
Photoelectron Emission ◽  
The Fourier Transform ◽  
The Relationship

To determine the thermodynamic temperature of a solid surface from the electron energy distribution measured by photoelectron spectroscopy, it is necessary to accurately evaluate the energy broadening of the photoelectron spectrum and investigate its temperature dependence. Broadening functions in the photoelectron spectrum of Au(110)’s surface near the Fermi level were estimated successfully using the relationship between the Fourier transform and the convolution integral. The Fourier transform could simultaneously reduce the noise of the spectrum when the broadening function was derived. The derived function was in the form of a Gaussian, whose width depended on the thermodynamic temperature of the sample and became broader at higher temperatures. The results contribute to improve accuracy of the determination of thermodynamic temperature from the photoelectron spectrum and provide useful information on the temperature dependence of electron scattering in photoelectron emission processes.

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