scholarly journals Resonance classes of measures

1987 ◽  
Vol 10 (3) ◽  
pp. 461-471 ◽  
Author(s):  
Maria Torres De Squire
Keyword(s):  
Fourier Analysis ◽  
Real Line ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Locally Compact ◽  
The Real ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups ◽  
Definition Of ◽  
Amalgam Spaces

We extendF. Holland's definition of the space of resonant classes of functions, on the real line, to the spaceR(Φpq) (1≦p, q≦∞)of resonant classes of measures, on locally compact abelian groups. We characterize this space in terms of transformable measures and establish a realatlonship betweenR(Φpq)and the set of positive definite functions for amalgam spaces. As a consequence we answer the conjecture posed by L. Argabright and J. Gil de Lamadrid in their work on Fourier analysis of unbounded measures.

Positive Definite Measures with Discrete Fourier Transform and Pure Point Diffraction

2011 ◽  
Vol 54 (3) ◽  
pp. 544-555 ◽  
Author(s):  
Nicolae Strungaru
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Abelian Groups ◽  
Positive Definite ◽  
Pure Point ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups

AbstractIn this paper we characterize the positive definite measures with discrete Fourier transform. As an application we provide a characterization of pure point diffraction in locally compact Abelian groups.

Positive Definiteness on Products of Compact Two-point Homogeneous Spaces and Locally Compact Abelian Groups

2019 ◽  
Vol 63 (4) ◽  
pp. 705-715
Author(s):  
V. A. Menegatto ◽  
C. P. Oliveira
Keyword(s):  
Homogeneous Spaces ◽  
Abelian Groups ◽  
Geodesic Distance ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Profile Function ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups

AbstractIn this paper, we consider the problem of characterizing positive definite functions on compact two-point homogeneous spaces cross locally compact abelian groups. For a locally compact abelian group $G$ with dual group $\widehat{G}$, a compact two-point homogeneous space $\mathbb{H}$ with normalized geodesic distance $\unicode[STIX]{x1D6FF}$ and a profile function $\unicode[STIX]{x1D719}:[-1,1]\times G\rightarrow \mathbb{C}$ satisfying certain continuity and integrability assumptions, we show that the positive definiteness of the kernel $((x,u),(y,v))\in (\mathbb{H}\times G)^{2}\mapsto \unicode[STIX]{x1D719}(\cos \unicode[STIX]{x1D6FF}(x,y),uv^{-1})$ is equivalent to the positive definiteness of the Fourier transformed kernels $(x,y)\in \mathbb{H}^{2}\mapsto \widehat{\unicode[STIX]{x1D719}}_{\cos \unicode[STIX]{x1D6FF}(x,y)}(\unicode[STIX]{x1D6FE})$, $\unicode[STIX]{x1D6FE}\in \widehat{G}$, where $\unicode[STIX]{x1D719}_{t}(u)=\unicode[STIX]{x1D719}(t,u)$, $u\in G$. We also provide some results on the strict positive definiteness of the kernel.

Strictly and Strongly Positive Definite Functions on Locally Compact Hypergroups

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
László Székelyhidi ◽  
Seyyed Mohammad Tabatabaie ◽  
Kedumetse Vati
Keyword(s):  
Positive Definite ◽  
Positive Definite Functions ◽  
Locally Compact
Sign in / Sign up

Export Citation Format

Share Document